LMFDB - Embedded newform 845.2.o.e.587.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(258,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.258"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.o (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,-4,-2,-6,-6,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			587.5
Root			$2.25081i$ of defining polynomial
Character	$\chi$	$=$	845.587
Dual form			845.2.o.e.488.5

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.12540 + 1.94926i) q^{2} +(-1.91913 - 0.514229i) q^{3} +(-1.53307 + 2.65535i) q^{4} +(-2.22228 - 0.247944i) q^{5} +(-1.15743 - 4.31958i) q^{6} +(1.10607 + 0.638592i) q^{7} -2.39966 q^{8} +(0.820542 + 0.473740i) q^{9} +(-2.01765 - 4.61083i) q^{10} +(1.41373 - 5.27612i) q^{11} +(4.30760 - 4.30760i) q^{12} +2.87469i q^{14} +(4.13734 + 1.61860i) q^{15} +(0.365551 + 0.633152i) q^{16} +(-0.833802 - 3.11179i) q^{17} +2.13259i q^{18} +(-1.17707 + 0.315395i) q^{19} +(4.06528 - 5.52081i) q^{20} +(-1.79431 - 1.79431i) q^{21} +(11.8755 - 3.18204i) q^{22} +(-0.0428736 + 0.160006i) q^{23} +(4.60524 + 1.23397i) q^{24} +(4.87705 + 1.10200i) q^{25} +(2.88358 + 2.88358i) q^{27} +(-3.39137 + 1.95801i) q^{28} +(8.41068 - 4.85591i) q^{29} +(1.50111 + 9.88630i) q^{30} +(0.233305 - 0.233305i) q^{31} +(-3.22244 + 5.58143i) q^{32} +(-5.42627 + 9.39857i) q^{33} +(5.12732 - 5.12732i) q^{34} +(-2.29967 - 1.69337i) q^{35} +(-2.51589 + 1.45255i) q^{36} +(1.14457 - 0.660816i) q^{37} +(-1.93947 - 1.93947i) q^{38} +(5.33270 + 0.594981i) q^{40} +(-0.483595 - 0.129579i) q^{41} +(1.47825 - 5.51690i) q^{42} +(6.43569 - 1.72444i) q^{43} +(11.8426 + 11.8426i) q^{44} +(-1.70601 - 1.25623i) q^{45} +(-0.360144 + 0.0965002i) q^{46} +3.20027i q^{47} +(-0.375953 - 1.40308i) q^{48} +(-2.68440 - 4.64952i) q^{49} +(3.34056 + 10.7468i) q^{50} +6.40069i q^{51} +(4.49845 - 4.49845i) q^{53} +(-2.37565 + 8.86603i) q^{54} +(-4.44989 + 11.3745i) q^{55} +(-2.65420 - 1.53240i) q^{56} +2.42113 q^{57} +(18.9308 + 10.9297i) q^{58} +(0.000595178 + 0.00222123i) q^{59} +(-10.6407 + 8.50465i) q^{60} +(-0.695993 + 1.20550i) q^{61} +(0.717332 + 0.192209i) q^{62} +(0.605053 + 1.04798i) q^{63} -13.0440 q^{64} -24.4270 q^{66} +(-3.03718 - 5.26055i) q^{67} +(9.54117 + 2.55655i) q^{68} +(0.164560 - 0.285026i) q^{69} +(0.712764 - 6.38837i) q^{70} +(-3.14648 - 11.7428i) q^{71} +(-1.96902 - 1.13681i) q^{72} +7.34614 q^{73} +(2.57620 + 1.48737i) q^{74} +(-8.79299 - 4.62280i) q^{75} +(0.967044 - 3.60906i) q^{76} +(4.93298 - 4.93298i) q^{77} -11.1774i q^{79} +(-0.655369 - 1.49768i) q^{80} +(-5.47236 - 9.47841i) q^{81} +(-0.291657 - 1.08848i) q^{82} -2.65539i q^{83} +(7.51533 - 2.01373i) q^{84} +(1.08139 + 7.12201i) q^{85} +(10.6041 + 10.6041i) q^{86} +(-18.6382 + 4.99409i) q^{87} +(-3.39247 + 12.6609i) q^{88} +(-6.96542 - 1.86638i) q^{89} +(0.528764 - 4.73922i) q^{90} +(-0.359145 - 0.359145i) q^{92} +(-0.567713 + 0.327769i) q^{93} +(-6.23815 + 3.60160i) q^{94} +(2.69398 - 0.409048i) q^{95} +(9.05440 - 9.05440i) q^{96} +(-2.09035 + 3.62059i) q^{97} +(6.04207 - 10.4652i) q^{98} +(3.65954 - 3.65954i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 4 q^{6} + 6 q^{7} + 12 q^{8} + 12 q^{9} + 2 q^{10} + 8 q^{11} + 24 q^{12} + 12 q^{15} - 2 q^{16} - 4 q^{17} - 16 q^{19} + 8 q^{20} + 4 q^{21} + 16 q^{22} + 10 q^{23}+ \cdots - 60 q^{99}+O(q^{100}) $ 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 4 * q^6 + 6 * q^7 + 12 * q^8 + 12 * q^9 + 2 * q^10 + 8 * q^11 + 24 * q^12 + 12 * q^15 - 2 * q^16 - 4 * q^17 - 16 * q^19 + 8 * q^20 + 4 * q^21 + 16 * q^22 + 10 * q^23 + 28 * q^24 - 18 * q^25 + 4 * q^27 - 6 * q^28 + 26 * q^30 - 6 * q^32 - 18 * q^33 - 2 * q^34 + 40 * q^35 - 36 * q^36 - 42 * q^37 + 8 * q^38 - 16 * q^40 + 28 * q^41 + 40 * q^42 - 10 * q^43 + 36 * q^44 - 32 * q^45 - 8 * q^46 - 56 * q^48 - 18 * q^49 + 8 * q^50 - 10 * q^53 - 12 * q^54 - 10 * q^55 - 12 * q^57 + 90 * q^58 - 8 * q^59 - 92 * q^60 - 16 * q^61 + 44 * q^62 - 32 * q^63 - 20 * q^64 - 32 * q^66 - 58 * q^67 + 22 * q^68 + 16 * q^69 + 32 * q^70 + 56 * q^71 + 66 * q^72 + 72 * q^73 + 18 * q^74 + 38 * q^75 + 80 * q^76 + 28 * q^77 + 68 * q^80 - 14 * q^81 - 56 * q^82 - 32 * q^84 + 6 * q^85 + 60 * q^86 - 34 * q^87 - 82 * q^88 + 6 * q^89 - 46 * q^90 - 8 * q^92 - 48 * q^93 - 48 * q^94 + 26 * q^95 + 56 * q^96 - 22 * q^97 + 4 * q^98 - 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.12540	+	1.94926i	0.795780	+	1.37833i	0.922342	+	0.386373i	$0.126272\pi$
$2$	1.12540	+	1.94926i	0.795780	+	1.37833i	−0.126562	+	0.991959i	$0.540394\pi$
$3$	−1.91913	−	0.514229i	−1.10801	−	0.296890i	−0.341987	−	0.939705i	$-0.611100\pi$
$3$	−1.91913	−	0.514229i	−1.10801	−	0.296890i	−0.766022	+	0.642815i	$0.777767\pi$
$4$	−1.53307	+	2.65535i	−0.766533	+	1.32767i
$5$	−2.22228	−	0.247944i	−0.993833	−	0.110884i
$5$	−2.22228	−	0.247944i	−0.993833	−	0.110884i
$6$	−1.15743	−	4.31958i	−0.472518	−	1.76346i
$7$	1.10607	+	0.638592i	0.418057	+	0.241365i	0.694245	−	0.719738i	$-0.255738\pi$
$7$	1.10607	+	0.638592i	0.418057	+	0.241365i	−0.276189	+	0.961103i	$0.589072\pi$
$8$	−2.39966			−0.848406
$9$	0.820542	+	0.473740i	0.273514	+	0.157913i
$10$	−2.01765	−	4.61083i	−0.638038	−	1.45807i
$11$	1.41373	−	5.27612i	0.426257	−	1.59081i	−0.334907	−	0.942251i	$-0.608705\pi$
$11$	1.41373	−	5.27612i	0.426257	−	1.59081i	0.761163	−	0.648560i	$-0.224629\pi$
$12$	4.30760	−	4.30760i	1.24350	−	1.24350i
$13$		0			0
$13$		0			0
$14$			2.87469i			0.768294i
$15$	4.13734	+	1.61860i	1.06826	+	0.417920i
$16$	0.365551	+	0.633152i	0.0913876	+	0.158288i
$17$	−0.833802	−	3.11179i	−0.202227	−	0.754721i	−0.990277	−	0.139110i	$-0.955576\pi$
$17$	−0.833802	−	3.11179i	−0.202227	−	0.754721i	0.788050	−	0.615611i	$-0.211091\pi$
$18$			2.13259i			0.502657i
$19$	−1.17707	+	0.315395i	−0.270039	+	0.0723567i	−0.391297	−	0.920264i	$-0.627974\pi$
$19$	−1.17707	+	0.315395i	−0.270039	+	0.0723567i	0.121259	+	0.992621i	$0.461307\pi$
$20$	4.06528	−	5.52081i	0.909024	−	1.23449i
$21$	−1.79431	−	1.79431i	−0.391551	−	0.391551i
$22$	11.8755	−	3.18204i	2.53187	−	0.678413i
$23$	−0.0428736	+	0.160006i	−0.00893976	+	0.0333637i	−0.970252	−	0.242099i	$-0.922164\pi$
$23$	−0.0428736	+	0.160006i	−0.00893976	+	0.0333637i	0.961312	+	0.275462i	$0.0888309\pi$
$24$	4.60524	+	1.23397i	0.940042	+	0.251883i
$25$	4.87705	+	1.10200i	0.975409	+	0.220401i
$26$		0			0
$27$	2.88358	+	2.88358i	0.554946	+	0.554946i
$28$	−3.39137	+	1.95801i	−0.640908	+	0.370029i
$29$	8.41068	−	4.85591i	1.56182	−	0.901719i	0.564751	−	0.825262i	$-0.308972\pi$
$29$	8.41068	−	4.85591i	1.56182	−	0.901719i	0.997073	−	0.0764575i	$-0.0243610\pi$
$30$	1.50111	+	9.88630i	0.274065	+	1.80498i
$31$	0.233305	−	0.233305i	0.0419027	−	0.0419027i	−0.685845	−	0.727748i	$-0.740567\pi$
$31$	0.233305	−	0.233305i	0.0419027	−	0.0419027i	0.727748	+	0.685845i	$0.240567\pi$
$32$	−3.22244	+	5.58143i	−0.569652	+	0.986667i
$33$	−5.42627	+	9.39857i	−0.944592	+	1.63608i
$34$	5.12732	−	5.12732i	0.879328	−	0.879328i
$35$	−2.29967	−	1.69337i	−0.388715	−	0.286232i
$36$	−2.51589	+	1.45255i	−0.419315	+	0.242091i
$37$	1.14457	−	0.660816i	0.188166	−	0.108638i	−0.402958	−	0.915219i	$-0.632018\pi$
$37$	1.14457	−	0.660816i	0.188166	−	0.108638i	0.591124	+	0.806581i	$0.298685\pi$
$38$	−1.93947	−	1.93947i	−0.314623	−	0.314623i
$39$		0			0
$40$	5.33270	+	0.594981i	0.843175	+	0.0940747i
$41$	−0.483595	−	0.129579i	−0.0755249	−	0.0202368i	0.220859	−	0.975306i	$-0.429114\pi$
$41$	−0.483595	−	0.129579i	−0.0755249	−	0.0202368i	−0.296384	+	0.955069i	$0.595781\pi$
$42$	1.47825	−	5.51690i	0.228099	−	0.851277i
$43$	6.43569	−	1.72444i	0.981434	−	0.262974i	0.267786	−	0.963479i	$-0.413708\pi$
$43$	6.43569	−	1.72444i	0.981434	−	0.262974i	0.713648	+	0.700504i	$0.247041\pi$
$44$	11.8426	+	11.8426i	1.78534	+	1.78534i
$45$	−1.70601	−	1.25623i	−0.254317	−	0.187268i
$46$	−0.360144	+	0.0965002i	−0.0531003	+	0.0142282i
$47$			3.20027i			0.466808i	0.972380	+	0.233404i	$0.0749864\pi$
$47$			3.20027i			0.466808i	−0.972380	+	0.233404i	$0.925014\pi$
$48$	−0.375953	−	1.40308i	−0.0542642	−	0.202517i
$49$	−2.68440	−	4.64952i	−0.383486	−	0.664217i
$50$	3.34056	+	10.7468i	0.472427	+	1.51983i
$51$			6.40069i			0.896276i
$52$		0			0
$53$	4.49845	−	4.49845i	0.617909	−	0.617909i	−0.327086	−	0.944995i	$-0.606067\pi$
$53$	4.49845	−	4.49845i	0.617909	−	0.617909i	0.944995	+	0.327086i	$0.106067\pi$
$54$	−2.37565	+	8.86603i	−0.323285	+	1.20651i
$55$	−4.44989	+	11.3745i	−0.600024	+	1.53374i
$56$	−2.65420	−	1.53240i	−0.354682	−	0.204776i
$57$	2.42113			0.320687
$58$	18.9308	+	10.9297i	2.48574	+	1.43514i
$59$	0.000595178		0.00222123i	7.74855e−5		0.000289180i	0.965965	−	0.258674i	$-0.0832857\pi$
$59$	0.000595178		0.00222123i	7.74855e−5		0.000289180i	−0.965887	+	0.258964i	$0.916619\pi$
$60$	−10.6407	+	8.50465i	−1.37371	+	1.09795i
$61$	−0.695993	+	1.20550i	−0.0891128	+	0.154348i	−0.907136	−	0.420837i	$-0.861736\pi$
$61$	−0.695993	+	1.20550i	−0.0891128	+	0.154348i	0.818024	+	0.575185i	$0.195070\pi$
$62$	0.717332	+	0.192209i	0.0911013	+	0.0244105i
$63$	0.605053	+	1.04798i	0.0762295	+	0.132033i
$64$	−13.0440			−1.63050
$65$		0			0
$66$	−24.4270			−3.00675
$67$	−3.03718	−	5.26055i	−0.371050	−	0.642678i	0.618677	−	0.785645i	$-0.287669\pi$
$67$	−3.03718	−	5.26055i	−0.371050	−	0.642678i	−0.989727	+	0.142967i	$0.954336\pi$
$68$	9.54117	+	2.55655i	1.15704	+	0.310027i
$69$	0.164560	−	0.285026i	0.0198107	−	0.0343131i
$70$	0.712764	−	6.38837i	0.0851916	−	0.763557i
$71$	−3.14648	−	11.7428i	−0.373418	−	1.39361i	−0.855643	−	0.517567i	$-0.826838\pi$
$71$	−3.14648	−	11.7428i	−0.373418	−	1.39361i	0.482225	−	0.876048i	$-0.339829\pi$
$72$	−1.96902	−	1.13681i	−0.232051	−	0.133975i
$73$	7.34614			0.859801			0.429901	−	0.902876i	$-0.358549\pi$
$73$	7.34614			0.859801			0.429901	+	0.902876i	$0.358549\pi$
$74$	2.57620	+	1.48737i	0.299477	+	0.172903i
$75$	−8.79299	−	4.62280i	−1.01533	−	0.533795i
$76$	0.967044	−	3.60906i	0.110928	−	0.413987i
$77$	4.93298	−	4.93298i	0.562166	−	0.562166i
$78$		0			0
$79$		−	11.1774i		−	1.25756i	−0.777584	−	0.628779i	$-0.783555\pi$
$79$		−	11.1774i		−	1.25756i	0.777584	−	0.628779i	$-0.216445\pi$
$80$	−0.655369	−	1.49768i	−0.0732725	−	0.167445i
$81$	−5.47236	−	9.47841i	−0.608040	−	1.05316i
$82$	−0.291657	−	1.08848i	−0.0322081	−	0.120202i
$83$		−	2.65539i		−	0.291467i	−0.989324	−	0.145733i	$-0.953446\pi$
$83$		−	2.65539i		−	0.291467i	0.989324	−	0.145733i	$-0.0465542\pi$
$84$	7.51533	−	2.01373i	0.819990	−	0.219716i
$85$	1.08139	+	7.12201i	0.117293	+	0.772490i
$86$	10.6041	+	10.6041i	1.14347	+	1.14347i
$87$	−18.6382	+	4.99409i	−1.99823	+	0.535423i
$88$	−3.39247	+	12.6609i	−0.361639	+	1.34965i
$89$	−6.96542	−	1.86638i	−0.738333	−	0.197836i	−0.129996	−	0.991515i	$-0.541496\pi$
$89$	−6.96542	−	1.86638i	−0.738333	−	0.197836i	−0.608337	+	0.793679i	$0.708163\pi$
$90$	0.528764	−	4.73922i	0.0557367	−	0.499558i
$91$		0			0
$92$	−0.359145	−	0.359145i	−0.0374434	−	0.0374434i
$93$	−0.567713	+	0.327769i	−0.0588691	+	0.0339881i
$94$	−6.23815	+	3.60160i	−0.643416	+	0.371477i
$95$	2.69398	−	0.409048i	0.276397	−	0.0419675i
$96$	9.05440	−	9.05440i	0.924111	−	0.924111i
$97$	−2.09035	+	3.62059i	−0.212243	+	0.367616i	−0.952416	−	0.304801i	$-0.901410\pi$
$97$	−2.09035	+	3.62059i	−0.212243	+	0.367616i	0.740173	+	0.672416i	$0.234743\pi$
$98$	6.04207	−	10.4652i	0.610341	−	1.05714i
$99$	3.65954	−	3.65954i	0.367797	−	0.367797i
$100$	−10.4030	+	11.2608i	−1.04030	+	1.12608i
$101$	7.47319	−	4.31465i	0.743610	−	0.429323i	−0.0797704	−	0.996813i	$-0.525419\pi$
$101$	7.47319	−	4.31465i	0.743610	−	0.429323i	0.823380	+	0.567490i	$0.192085\pi$
$102$	−12.4766	+	7.20336i	−1.23537	+	0.713239i
$103$	−1.07603	−	1.07603i	−0.106025	−	0.106025i	0.652104	−	0.758129i	$-0.273886\pi$
$103$	−1.07603	−	1.07603i	−0.106025	−	0.106025i	−0.758129	+	0.652104i	$0.773886\pi$
$104$		0			0
$105$	3.54258	+	4.43236i	0.345720	+	0.432554i
$106$	13.8312	+	3.70606i	1.34340	+	0.359964i
$107$	3.75956	−	14.0309i	0.363451	−	1.35642i	−0.506058	−	0.862499i	$-0.668898\pi$
$107$	3.75956	−	14.0309i	0.363451	−	1.35642i	0.869509	−	0.493917i	$-0.164435\pi$
$108$	−12.0776	+	3.23619i	−1.16217	+	0.311403i
$109$	4.72405	+	4.72405i	0.452481	+	0.452481i	0.896177	−	0.443696i	$-0.146333\pi$
$109$	4.72405	+	4.72405i	0.452481	+	0.452481i	−0.443696	+	0.896177i	$0.646333\pi$
$110$	−27.1797	+	4.12691i	−2.59149	+	0.393486i
$111$	−2.53638	+	0.679621i	−0.240743	+	0.0645068i
$112$			0.933751i			0.0882311i
$113$	2.94919	+	11.0065i	0.277437	+	1.03541i	0.954191	+	0.299199i	$0.0967193\pi$
$113$	2.94919	+	11.0065i	0.277437	+	1.03541i	−0.676754	+	0.736209i	$0.736614\pi$
$114$	2.72475	+	4.71941i	0.255197	+	0.442013i
$115$	0.134950	−	0.344949i	0.0125841	−	0.0321666i
$116$			29.7777i			2.76479i
$117$		0			0
$118$	−0.00365994	+	0.00365994i	−0.000336925	+	0.000336925i
$119$	1.06492	−	3.97433i	0.0976210	−	0.364326i
$120$	−9.92818	−	3.88407i	−0.906315	−	0.354566i
$121$	−16.3126	−	9.41807i	−1.48296	−	0.856188i
$122$	−3.13309			−0.283657
$123$	0.861447	+	0.497357i	0.0776741	+	0.0448452i
$124$	0.261833	+	0.977176i	0.0235133	+	0.0877530i
$125$	−10.5649	−	3.65819i	−0.944956	−	0.327199i
$126$	−1.36186	+	2.35881i	−0.121324	+	0.210139i
$127$	0.506651	+	0.135757i	0.0449580	+	0.0120465i	0.281228	−	0.959641i	$-0.409258\pi$
$127$	0.506651	+	0.135757i	0.0449580	+	0.0120465i	−0.236270	+	0.971687i	$0.575925\pi$
$128$	−8.23486	−	14.2632i	−0.727865	−	1.26070i
$129$	−13.2377			−1.16551
$130$		0			0
$131$	5.09883			0.445486			0.222743	−	0.974877i	$-0.428499\pi$
$131$	5.09883			0.445486			0.222743	+	0.974877i	$0.428499\pi$
$132$	−16.6377	−	28.8173i	−1.44812	−	2.50822i
$133$	−1.50334	−	0.402818i	−0.130356	−	0.0349287i
$134$	6.83610	−	11.8405i	0.590549	−	1.02286i
$135$	−5.69316	−	7.12309i	−0.489989	−	0.613058i
$136$	2.00084	+	7.46723i	0.171571	+	0.640310i
$137$	−3.29390	−	1.90173i	−0.281417	−	0.162476i	0.352648	−	0.935756i	$-0.385281\pi$
$137$	−3.29390	−	1.90173i	−0.281417	−	0.162476i	−0.634065	+	0.773280i	$0.718615\pi$
$138$	0.740785			0.0630598
$139$	−1.28017	−	0.739106i	−0.108583	−	0.0626902i	0.444725	−	0.895667i	$-0.353301\pi$
$139$	−1.28017	−	0.739106i	−0.108583	−	0.0626902i	−0.553308	+	0.832977i	$0.686635\pi$
$140$	8.02204	−	3.51037i	0.677986	−	0.296680i
$141$	1.64567	−	6.14173i	0.138591	−	0.517227i
$142$	19.3487	−	19.3487i	1.62371	−	1.62371i
$143$		0			0
$144$			0.692704i			0.0577253i
$145$	−19.8949	+	8.70580i	−1.65218	+	0.722977i
$146$	8.26737	+	14.3195i	0.684213	+	1.18509i
$147$	2.76079	+	10.3034i	0.227706	+	0.849811i
$148$			4.05230i			0.333097i
$149$	−16.6295	+	4.45586i	−1.36234	+	0.365038i	−0.864675	−	0.502331i	$-0.832476\pi$
$149$	−16.6295	+	4.45586i	−1.36234	+	0.365038i	−0.497665	+	0.867369i	$0.665809\pi$
$150$	−0.884644	−	22.3423i	−0.0722308	−	1.82424i
$151$	−10.0539	−	10.0539i	−0.818178	−	0.818178i	0.167666	−	0.985844i	$-0.446377\pi$
$151$	−10.0539	−	10.0539i	−0.818178	−	0.818178i	−0.985844	+	0.167666i	$0.946377\pi$
$152$	2.82457	−	0.756840i	0.229103	−	0.0613879i
$153$	0.790011	−	2.94836i	0.0638686	−	0.238361i
$154$	15.1672	+	4.06405i	1.22221	+	0.327491i
$155$	−0.576314	+	0.460621i	−0.0462907	+	0.0369980i
$156$		0			0
$157$	3.07230	+	3.07230i	0.245196	+	0.245196i	0.818996	−	0.573799i	$-0.194531\pi$
$157$	3.07230	+	3.07230i	0.245196	+	0.245196i	−0.573799	+	0.818996i	$0.694531\pi$
$158$	21.7876	−	12.5791i	1.73333	−	1.00074i
$159$	−10.9463	+	6.31986i	−0.868100	+	0.501198i
$160$	8.54504	−	11.6045i	0.675545	−	0.917417i
$161$	−0.149600	+	0.149600i	−0.0117902	+	0.0117902i
$162$	12.3172	−	21.3341i	0.967733	−	1.67616i
$163$	−4.60251	+	7.97177i	−0.360496	+	0.624398i	−0.988043	−	0.154182i	$-0.950726\pi$
$163$	−4.60251	+	7.97177i	−0.360496	+	0.624398i	0.627546	+	0.778579i	$0.284059\pi$
$164$	1.08546	−	1.08546i	0.0847602	−	0.0847602i
$165$	14.3890	−	19.5408i	1.12018	−	1.52125i
$166$	5.17603	−	2.98838i	0.401738	−	0.231944i
$167$	−10.9455	+	6.31936i	−0.846985	+	0.489007i	−0.859632	−	0.510913i	$-0.829307\pi$
$167$	−10.9455	+	6.31936i	−0.846985	+	0.489007i	0.0126474	+	0.999920i	$0.495974\pi$
$168$	4.30574	+	4.30574i	0.332195	+	0.332195i
$169$		0			0
$170$	−12.6656	+	10.1230i	−0.971409	+	0.776402i
$171$	−1.11525	−	0.298831i	−0.0852854	−	0.0228522i
$172$	−5.28736	+	19.7327i	−0.403157	+	1.50460i
$173$	13.2481	−	3.54983i	1.00724	−	0.269888i	0.282762	−	0.959190i	$-0.408749\pi$
$173$	13.2481	−	3.54983i	1.00724	−	0.269888i	0.724474	+	0.689302i	$0.242083\pi$
$174$	−30.7103	−	30.7103i	−2.32814	−	2.32814i
$175$	4.69064	+	4.33334i	0.354579	+	0.327570i
$176$	3.85738	−	1.03358i	0.290761	−	0.0779092i
$177$		−	0.00456889i		−	0.000343419i
$178$	−4.20086	−	15.6778i	−0.314867	−	1.17510i
$179$	6.32126	+	10.9487i	0.472473	+	0.818347i	0.999504	−	0.0314989i	$-0.0100281\pi$
$179$	6.32126	+	10.9487i	0.472473	+	0.818347i	−0.527031	+	0.849846i	$0.676695\pi$
$180$	5.95116	−	2.60417i	0.443573	−	0.194103i
$181$			8.16619i			0.606988i	0.952833	+	0.303494i	$0.0981533\pi$
$181$			8.16619i			0.606988i	−0.952833	+	0.303494i	$0.901847\pi$
$182$		0			0
$183$	1.95560	−	1.95560i	0.144562	−	0.144562i
$184$	0.102882	−	0.383960i	0.00758455	−	0.0283059i
$185$	−2.70739	+	1.18473i	−0.199052	+	0.0871030i
$186$	−1.27781	−	0.737745i	−0.0936937	−	0.0540941i
$187$	−17.5970			−1.28682
$188$	−8.49784	−	4.90623i	−0.619769	−	0.357824i
$189$	1.34802	+	5.03089i	0.0980542	+	0.365943i
$190$	3.82916	+	4.79091i	0.277796	+	0.347569i
$191$	7.37692	−	12.7772i	0.533775	−	0.924526i	−0.465446	−	0.885076i	$-0.654106\pi$
$191$	7.37692	−	12.7772i	0.533775	−	0.924526i	0.999222	−	0.0394498i	$-0.0125605\pi$
$192$	25.0330	+	6.70758i	1.80660	+	0.484078i
$193$	7.54845	+	13.0743i	0.543349	+	0.941109i	0.998709	+	0.0508011i	$0.0161775\pi$
$193$	7.54845	+	13.0743i	0.543349	+	0.941109i	−0.455359	+	0.890308i	$0.650489\pi$
$194$	−9.40995			−0.675595
$195$		0			0
$196$	16.4614			1.17582
$197$	7.68576	+	13.3121i	0.547588	+	0.948450i	0.998439	+	0.0558510i	$0.0177872\pi$
$197$	7.68576	+	13.3121i	0.547588	+	0.948450i	−0.450851	+	0.892599i	$0.648879\pi$
$198$	11.2518	+	3.01492i	0.799633	+	0.214261i
$199$	−5.72810	+	9.92136i	−0.406054	+	0.703307i	−0.994444	−	0.105271i	$-0.966429\pi$
$199$	−5.72810	+	9.92136i	−0.406054	+	0.703307i	0.588389	+	0.808578i	$0.299762\pi$
$200$	−11.7032	−	2.64443i	−0.827544	−	0.186989i
$201$	3.12361	+	11.6575i	0.220322	+	0.822254i
$202$	16.8207	+	9.71144i	1.18350	+	0.683294i
$203$	12.4038			0.870574
$204$	−16.9961	−	9.81268i	−1.18996	−	0.687025i
$205$	1.04255	+	0.407865i	0.0728152	+	0.0284865i
$206$	0.886492	−	3.30843i	0.0617648	−	0.230509i
$207$	−0.110981	+	0.110981i	−0.00771372	+	0.00771372i
$208$		0			0
$209$			6.65626i			0.460423i
$210$	−4.65297	+	11.8936i	−0.321085	+	0.820735i
$211$	−1.59195	−	2.75735i	−0.109595	−	0.189823i	0.806011	−	0.591900i	$-0.201622\pi$
$211$	−1.59195	−	2.75735i	−0.109595	−	0.189823i	−0.915606	+	0.402076i	$0.868289\pi$
$212$	5.04852	+	18.8414i	0.346734	+	1.29403i
$213$			24.1539i			1.65500i
$214$	31.5808	−	8.46205i	2.15882	−	0.578454i
$215$	−14.7295	+	2.23649i	−1.00454	+	0.152527i
$216$	−6.91961	−	6.91961i	−0.470820	−	0.470820i
$217$	0.407038	−	0.109066i	0.0276316	−	0.00740386i
$218$	−3.89192	+	14.5248i	−0.263594	+	0.983746i
$219$	−14.0982	−	3.77760i	−0.952667	−	0.255266i
$220$	−23.3813	−	29.2539i	−1.57636	−	1.97230i
$221$		0			0
$222$	−4.17921	−	4.17921i	−0.280490	−	0.280490i
$223$	10.2862	−	5.93874i	0.688815	−	0.397688i	−0.114353	−	0.993440i	$-0.536479\pi$
$223$	10.2862	−	5.93874i	0.688815	−	0.397688i	0.803168	+	0.595753i	$0.203146\pi$
$224$	−7.12851	+	4.11565i	−0.476294	+	0.274988i
$225$	3.47976	+	3.21469i	0.231984	+	0.214313i
$226$	−18.1355	+	18.1355i	−1.20636	+	1.20636i
$227$	13.8333	−	23.9600i	0.918149	−	1.59028i	0.115924	−	0.993258i	$-0.463017\pi$
$227$	13.8333	−	23.9600i	0.918149	−	1.59028i	0.802225	−	0.597022i	$-0.203650\pi$
$228$	−3.71176	+	6.42896i	−0.245817	+	0.425768i
$229$	−12.9000	+	12.9000i	−0.852455	+	0.852455i	−0.990435	−	0.137980i	$-0.955939\pi$
$229$	−12.9000	+	12.9000i	−0.852455	+	0.852455i	0.137980	+	0.990435i	$0.455939\pi$
$230$	0.824266	−	0.125155i	0.0543505	−	0.00825246i
$231$	−12.0037	+	6.93034i	−0.789786	+	0.455983i
$232$	−20.1827	+	11.6525i	−1.32506	+	0.765024i
$233$	16.3545	+	16.3545i	1.07142	+	1.07142i	0.997246	+	0.0741712i	$0.0236311\pi$
$233$	16.3545	+	16.3545i	1.07142	+	1.07142i	0.0741712	+	0.997246i	$0.476369\pi$
$234$		0			0
$235$	0.793489	−	7.11190i	0.0517615	−	0.463929i
$236$	−0.00681059	−	0.00182489i	−0.000443332	−	0.000118790i
$237$	−5.74774	+	21.4509i	−0.373356	+	1.39338i
$238$	8.94546	−	2.39693i	0.579848	−	0.155370i
$239$	2.61794	+	2.61794i	0.169341	+	0.169341i	0.786690	−	0.617349i	$-0.211793\pi$
$239$	2.61794	+	2.61794i	0.169341	+	0.169341i	−0.617349	+	0.786690i	$0.711793\pi$
$240$	0.487588	+	3.21124i	0.0314737	+	0.207285i
$241$	−20.1013	+	5.38613i	−1.29484	+	0.346951i	−0.839496	−	0.543365i	$-0.817150\pi$
$241$	−20.1013	+	5.38613i	−1.29484	+	0.346951i	−0.455343	+	0.890316i	$0.650483\pi$
$242$		−	42.3965i		−	2.72535i
$243$	2.46169	+	9.18717i	0.157918	+	0.589357i
$244$	−2.13401	−	3.69621i	−0.136616	−	0.236625i
$245$	4.81267	+	10.9981i	0.307470	+	0.702643i
$246$			2.23891i			0.142748i
$247$		0			0
$248$	−0.559851	+	0.559851i	−0.0355505	+	0.0355505i
$249$	−1.36548	+	5.09603i	−0.0865336	+	0.322948i
$250$	−4.75905	−	24.7107i	−0.300989	−	1.56284i
$251$	2.05050	+	1.18386i	0.129427	+	0.0747245i	0.563315	−	0.826242i	$-0.309526\pi$
$251$	2.05050	+	1.18386i	0.129427	+	0.0747245i	−0.433889	+	0.900966i	$0.642859\pi$
$252$	−3.71034			−0.233730
$253$	0.783602	+	0.452413i	0.0492647	+	0.0284430i
$254$	0.305562	+	1.14037i	0.0191727	+	0.0715533i
$255$	1.58701	−	14.2241i	0.0993827	−	0.890749i
$256$	5.49109	−	9.51085i	0.343193	−	0.594428i
$257$	−0.840391	−	0.225182i	−0.0524221	−	0.0140465i	0.232513	−	0.972593i	$-0.425305\pi$
$257$	−0.840391	−	0.225182i	−0.0524221	−	0.0140465i	−0.284935	+	0.958547i	$0.591972\pi$
$258$	−14.8977	−	25.8036i	−0.927492	−	1.60646i
$259$	1.68797			0.104885
$260$		0			0
$261$	9.20175			0.569574
$262$	5.73824	+	9.93892i	0.354509	+	0.614028i
$263$	14.6707	+	3.93099i	0.904632	+	0.242395i	0.681004	−	0.732279i	$-0.261543\pi$
$263$	14.6707	+	3.93099i	0.904632	+	0.242395i	0.223627	+	0.974675i	$0.428210\pi$
$264$	13.0212	−	22.5533i	0.801398	−	1.38806i
$265$	−11.1122	+	8.88144i	−0.682615	+	0.545582i
$266$	−0.906665	−	3.38372i	−0.0555912	−	0.207469i
$267$	12.4078	+	7.16363i	0.759343	+	0.438407i
$268$	18.6248			1.13769
$269$	21.1150	+	12.1908i	1.28741	+	0.743285i	0.978191	−	0.207707i	$-0.0666000\pi$
$269$	21.1150	+	12.1908i	1.28741	+	0.743285i	0.309216	+	0.950992i	$0.399933\pi$
$270$	7.47763	−	19.1138i	0.455074	−	1.16323i
$271$	3.39484	−	12.6697i	0.206222	−	0.769630i	−0.782852	−	0.622208i	$-0.786236\pi$
$271$	3.39484	−	12.6697i	0.206222	−	0.769630i	0.989074	−	0.147422i	$-0.0470975\pi$
$272$	1.66544	−	1.66544i	0.100982	−	0.100982i
$273$		0			0
$274$		−	8.56086i		−	0.517181i
$275$	12.7091	−	24.1740i	0.766390	−	1.45775i
$276$	0.504562	+	0.873927i	0.0303711	+	0.0526042i
$277$	−3.16472	−	11.8109i	−0.190149	−	0.709647i	−0.993469	−	0.114099i	$-0.963602\pi$
$277$	−3.16472	−	11.8109i	−0.190149	−	0.709647i	0.803320	−	0.595548i	$-0.203065\pi$
$278$		−	3.32717i		−	0.199550i
$279$	0.301962	−	0.0809104i	0.0180780	−	0.00484398i
$280$	5.51841	+	4.06352i	0.329788	+	0.242841i
$281$	−6.43529	−	6.43529i	−0.383897	−	0.383897i	0.488607	−	0.872504i	$-0.337505\pi$
$281$	−6.43529	−	6.43529i	−0.383897	−	0.383897i	−0.872504	+	0.488607i	$0.837505\pi$
$282$	13.8239	−	3.70409i	0.823198	−	0.220575i
$283$	−7.07953	+	26.4212i	−0.420834	+	1.57057i	0.352021	+	0.935992i	$0.385495\pi$
$283$	−7.07953	+	26.4212i	−0.420834	+	1.57057i	−0.772855	+	0.634583i	$0.781172\pi$
$284$	36.0050	+	9.64751i	2.13650	+	0.572474i
$285$	−5.38044	−	0.600307i	−0.318710	−	0.0355591i
$286$		0			0
$287$	−0.452144	−	0.452144i	−0.0266892	−	0.0266892i
$288$	−5.28829	+	3.05320i	−0.311616	+	0.179911i
$289$	5.73440	−	3.31076i	0.337318	−	0.194750i
$290$	−39.3596	−	28.9826i	−2.31127	−	1.70192i
$291$	5.87346	−	5.87346i	0.344308	−	0.344308i
$292$	−11.2621	+	19.5066i	−0.659066	+	1.14154i
$293$	13.0620	−	22.6241i	0.763092	−	1.32171i	−0.178157	−	0.984002i	$-0.557013\pi$
$293$	13.0620	−	22.6241i	0.763092	−	1.32171i	0.941249	−	0.337713i	$-0.109653\pi$
$294$	−16.9770	+	16.9770i	−0.990118	+	0.990118i
$295$	−0.000771909	−	0.00508377i	−4.49423e−5	−	0.000295989i
$296$	−2.74657	+	1.58573i	−0.159641	+	0.0921688i
$297$	19.2908	−	11.1375i	1.11936	−	0.646265i
$298$	−27.4005	−	27.4005i	−1.58727	−	1.58727i
$299$		0			0
$300$	25.7554	−	16.2614i	1.48699	−	0.938852i
$301$	8.21957	+	2.20243i	0.473768	+	0.126946i
$302$	8.28296	−	30.9124i	0.476631	−	1.77881i
$303$	−16.5607	+	4.43743i	−0.951388	+	0.254924i
$304$	−0.629972	−	0.629972i	−0.0361314	−	0.0361314i
$305$	1.84559	−	2.50638i	0.105678	−	0.143515i
$306$	6.63619	−	1.77816i	0.379366	−	0.101651i
$307$			14.7038i			0.839189i	0.907712	+	0.419595i	$0.137828\pi$
$307$			14.7038i			0.839189i	−0.907712	+	0.419595i	$0.862172\pi$
$308$	5.53620	+	20.6614i	0.315454	+	1.17729i
$309$	1.51172	+	2.61837i	0.0859985	+	0.148954i
$310$	−1.54645	−	0.604999i	−0.0878327	−	0.0343617i
$311$		−	31.8525i		−	1.80619i	−0.429440	−	0.903095i	$-0.641289\pi$
$311$		−	31.8525i		−	1.80619i	0.429440	−	0.903095i	$-0.358711\pi$
$312$		0			0
$313$	−11.9865	+	11.9865i	−0.677519	+	0.677519i	−0.959438	−	0.281919i	$-0.909029\pi$
$313$	−11.9865	+	11.9865i	−0.677519	+	0.677519i	0.281919	+	0.959438i	$0.409029\pi$
$314$	−2.53112	+	9.44628i	−0.142840	+	0.533084i
$315$	−1.08476	−	2.47893i	−0.0611190	−	0.139672i
$316$	29.6799	+	17.1357i	1.66963	+	0.963959i
$317$	15.5627			0.874088			0.437044	−	0.899440i	$-0.356025\pi$
$317$	15.5627			0.874088			0.437044	+	0.899440i	$0.356025\pi$
$318$	−24.6380	−	14.2248i	−1.38163	−	0.797686i
$319$	−13.7299	−	51.2407i	−0.768728	−	2.86893i
$320$	28.9874	+	3.23418i	1.62044	+	0.180796i
$321$	−14.4302	+	24.9938i	−0.805413	+	1.39502i
$322$	−0.459970	−	0.123249i	−0.0256331	−	0.00686837i
$323$	1.96289	+	3.39983i	0.109218	+	0.189171i
$324$	33.5580			1.86433
$325$		0			0
$326$	−20.7187			−1.14750
$327$	−6.63680	−	11.4953i	−0.367016	−	0.635691i
$328$	1.16046	+	0.310945i	0.0640758	+	0.0171691i
$329$	−2.04367	+	3.53974i	−0.112671	+	0.195152i
$330$	54.2835	+	6.05653i	2.98821	+	0.333401i
$331$	4.41633	+	16.4820i	0.242743	+	0.905930i	0.974504	+	0.224369i	$0.0720321\pi$
$331$	4.41633	+	16.4820i	0.242743	+	0.905930i	−0.731761	+	0.681561i	$0.761301\pi$
$332$	7.05098	+	4.07089i	0.386973	+	0.223419i
$333$	1.25222			0.0686212
$334$	−24.6361	−	14.2237i	−1.34803	−	0.778284i
$335$	5.44513	+	12.4435i	0.297499	+	0.679858i
$336$	0.480161	−	1.79199i	0.0261949	−	0.0977609i
$337$	−25.0560	+	25.0560i	−1.36489	+	1.36489i	−0.497319	+	0.867568i	$0.665682\pi$
$337$	−25.0560	+	25.0560i	−1.36489	+	1.36489i	−0.867568	+	0.497319i	$0.834318\pi$
$338$		0			0
$339$		−	22.6395i		−	1.22961i
$340$	−20.5693	−	8.04704i	−1.11552	−	0.436412i
$341$	−0.901114	−	1.56077i	−0.0487980	−	0.0845207i
$342$	−0.672610	−	2.51022i	−0.0363706	−	0.135737i
$343$		−	15.7972i		−	0.852971i
$344$	−15.4435	+	4.13806i	−0.832655	+	0.223109i
$345$	−0.436368	+	0.592605i	−0.0234933	+	0.0319048i
$346$	21.8290	+	21.8290i	1.17354	+	1.17354i
$347$	−12.4604	+	3.33874i	−0.668907	+	0.179233i	−0.577262	−	0.816559i	$-0.695879\pi$
$347$	−12.4604	+	3.33874i	−0.668907	+	0.179233i	−0.0916446	+	0.995792i	$0.529212\pi$
$348$	15.3125	−	57.1472i	0.820838	−	3.06341i
$349$	−25.9362	−	6.94957i	−1.38833	−	0.372002i	−0.514191	−	0.857676i	$-0.671908\pi$
$349$	−25.9362	−	6.94957i	−1.38833	−	0.372002i	−0.874140	+	0.485674i	$0.838574\pi$
$350$	−3.16792	+	14.0200i	−0.169332	+	0.749402i
$351$		0			0
$352$	24.8926	+	24.8926i	1.32678	+	1.32678i
$353$	−20.1885	+	11.6558i	−1.07453	+	0.620378i	−0.929414	−	0.369038i	$-0.879687\pi$
$353$	−20.1885	+	11.6558i	−1.07453	+	0.620378i	−0.145111	+	0.989415i	$0.546354\pi$
$354$	0.00890593	−	0.00514184i	0.000473345	−	0.000273286i
$355$	4.08078	+	26.8759i	0.216586	+	1.42643i
$356$	15.6343	−	15.6343i	0.828617	−	0.828617i
$357$	−4.08743	+	7.07964i	−0.216330	+	0.374694i
$358$	−14.2279	+	24.6435i	−0.751970	+	1.30245i
$359$	−9.17222	+	9.17222i	−0.484091	+	0.484091i	−0.906435	−	0.422344i	$-0.861207\pi$
$359$	−9.17222	+	9.17222i	−0.484091	+	0.484091i	0.422344	+	0.906435i	$0.361207\pi$
$360$	4.09384	+	3.01452i	0.215764	+	0.158879i
$361$	−15.1685	+	8.75751i	−0.798340	+	0.460922i
$362$	−15.9180	+	9.19026i	−0.836631	+	0.483029i
$363$	26.4629	+	26.4629i	1.38894	+	1.38894i
$364$		0			0
$365$	−16.3252	−	1.82143i	−0.854499	−	0.0953382i
$366$	6.01280	+	1.61113i	0.314294	+	0.0842149i
$367$	3.84780	−	14.3602i	0.200853	−	0.749595i	−0.789820	−	0.613338i	$-0.789826\pi$
$367$	3.84780	−	14.3602i	0.200853	−	0.749595i	0.990674	−	0.136256i	$-0.0435071\pi$
$368$	−0.116981	+	0.0313449i	−0.00609805	+	0.00163397i
$369$	−0.335423	−	0.335423i	−0.0174614	−	0.0174614i
$370$	−5.35625	−	3.94410i	−0.278458	−	0.205044i
$371$	7.84829	−	2.10294i	0.407463	−	0.109179i
$372$		−	2.00997i		−	0.104212i
$373$	1.59980	+	5.97055i	0.0828348	+	0.309144i	0.994895	−	0.100912i	$-0.0321760\pi$
$373$	1.59980	+	5.97055i	0.0828348	+	0.309144i	−0.912061	+	0.410055i	$0.865509\pi$
$374$	−19.8037	−	34.3010i	−1.02403	−	1.77366i
$375$	18.3943	+	12.4533i	0.949877	+	0.643087i
$376$		−	7.67955i		−	0.396043i
$377$		0			0
$378$	−8.28942	+	8.28942i	−0.426362	+	0.426362i
$379$	4.72834	−	17.6464i	0.242878	−	0.906435i	−0.731559	−	0.681778i	$-0.761207\pi$
$379$	4.72834	−	17.6464i	0.242878	−	0.906435i	0.974438	−	0.224657i	$-0.0721262\pi$
$380$	−3.04389	+	7.78056i	−0.156148	+	0.399134i
$381$	−0.902517	−	0.521068i	−0.0462373	−	0.0266951i
$382$	33.2081			1.69907
$383$	8.87106	+	5.12171i	0.453290	+	0.261707i	0.709219	−	0.704989i	$-0.249048\pi$
$383$	8.87106	+	5.12171i	0.453290	+	0.261707i	−0.255929	+	0.966696i	$0.582381\pi$
$384$	8.46920	+	31.6075i	0.432192	+	1.61296i
$385$	−12.1856	+	9.73936i	−0.621034	+	0.496364i
$386$	−16.9901	+	29.4277i	−0.864774	+	1.49783i
$387$	6.09769	+	1.63387i	0.309963	+	0.0830543i
$388$	−6.40929	−	11.1012i	−0.325382	−	0.563579i
$389$	3.41200			0.172995			0.0864977	−	0.996252i	$-0.472432\pi$
$389$	3.41200			0.172995			0.0864977	+	0.996252i	$0.472432\pi$
$390$		0			0
$391$	0.533655			0.0269881
$392$	6.44164	+	11.1572i	0.325352	+	0.563526i
$393$	−9.78529	−	2.62196i	−0.493603	−	0.132260i
$394$	−17.2992	+	29.9630i	−0.871519	+	1.50952i
$395$	−2.77138	+	24.8393i	−0.139443	+	1.24980i
$396$	4.10703	+	15.3277i	0.206386	+	0.770244i
$397$	10.3335	+	5.96603i	0.518622	+	0.299426i	0.736371	−	0.676578i	$-0.236538\pi$
$397$	10.3335	+	5.96603i	0.518622	+	0.299426i	−0.217749	+	0.976005i	$0.569871\pi$
$398$	−25.7857			−1.29252
$399$	2.67795	+	1.54612i	0.134065	+	0.0774027i
$400$	1.08507	+	3.49075i	0.0542536	+	0.174538i
$401$	−1.05497	+	3.93721i	−0.0526828	+	0.196615i	−0.987252	−	0.159168i	$-0.949119\pi$
$401$	−1.05497	+	3.93721i	−0.0526828	+	0.196615i	0.934569	+	0.355783i	$0.115786\pi$
$402$	−19.2081	+	19.2081i	−0.958011	+	0.958011i
$403$		0			0
$404$			26.4586i			1.31636i
$405$	9.81100	+	22.4205i	0.487512	+	1.11408i
$406$	13.9592	+	24.1781i	0.692786	+	1.19994i
$407$	−1.86844	−	6.97310i	−0.0926149	−	0.345644i
$408$		−	15.3595i		−	0.760406i
$409$	−6.70266	+	1.79597i	−0.331425	+	0.0888051i	−0.420694	−	0.907202i	$-0.638214\pi$
$409$	−6.70266	+	1.79597i	−0.331425	+	0.0888051i	0.0892692	+	0.996008i	$0.471547\pi$
$410$	0.378261	+	2.49122i	0.0186810	+	0.123033i
$411$	5.34348	+	5.34348i	0.263574	+	0.263574i
$412$	4.50687	−	1.20761i	0.222037	−	0.0594948i
$413$	−0.000760151		0.00283692i	−3.74046e−5		0.000139596i
$414$	−0.341229	−	0.0914320i	−0.0167705	−	0.00449364i
$415$	−0.658389	+	5.90102i	−0.0323190	+	0.289670i
$416$		0			0
$417$	2.07674	+	2.07674i	0.101698	+	0.101698i
$418$	−12.9748	+	7.49098i	−0.634616	+	0.366396i
$419$	−18.3846	+	10.6144i	−0.898147	+	0.518546i	−0.876599	−	0.481222i	$-0.840193\pi$
$419$	−18.3846	+	10.6144i	−0.898147	+	0.518546i	−0.0215487	+	0.999768i	$0.506860\pi$
$420$	−17.2004	+	2.61168i	−0.839296	+	0.127437i
$421$	−3.15727	+	3.15727i	−0.153876	+	0.153876i	−0.779847	−	0.625971i	$-0.784703\pi$
$421$	−3.15727	+	3.15727i	−0.153876	+	0.153876i	0.625971	+	0.779847i	$0.284703\pi$
$422$	3.58318	−	6.20625i	0.174427	−	0.302116i
$423$	−1.51610	+	2.62596i	−0.0737152	+	0.127678i
$424$	−10.7947	+	10.7947i	−0.524238	+	0.524238i
$425$	−0.637290	−	16.0952i	−0.0309131	−	0.780733i
$426$	−47.0822	+	27.1829i	−2.28114	+	1.31702i
$427$	−1.53964	+	0.888911i	−0.0745084	+	0.0430174i
$428$	31.4932	+	31.4932i	1.52228	+	1.52228i
$429$		0			0
$430$	−20.9361	−	26.1946i	−1.00963	−	1.26321i
$431$	−34.6226	−	9.27711i	−1.66771	−	0.446863i	−0.703221	−	0.710971i	$-0.748256\pi$
$431$	−34.6226	−	9.27711i	−1.66771	−	0.446863i	−0.964493	+	0.264109i	$0.914922\pi$
$432$	−0.771651	+	2.87984i	−0.0371261	+	0.138556i
$433$	−7.81733	+	2.09465i	−0.375677	+	0.100662i	−0.441716	−	0.897155i	$-0.645630\pi$
$433$	−7.81733	+	2.09465i	−0.375677	+	0.100662i	0.0660397	+	0.997817i	$0.478964\pi$
$434$	0.670679	+	0.670679i	0.0321936	+	0.0321936i
$435$	42.6575	−	6.47703i	2.04527	−	0.310550i
$436$	−19.7863	+	5.30171i	−0.947590	+	0.253906i
$437$		−	0.201861i		−	0.00965633i
$438$	−8.50264	−	31.7323i	−0.406272	−	1.51623i
$439$	−14.3336	−	24.8265i	−0.684104	−	1.18490i	−0.973717	−	0.227759i	$-0.926860\pi$
$439$	−14.3336	−	24.8265i	−0.684104	−	1.18490i	0.289613	−	0.957144i	$-0.406473\pi$
$440$	10.6782	−	27.2949i	0.509064	−	1.30123i
$441$		−	5.08683i		−	0.242230i
$442$		0			0
$443$	−17.1586	+	17.1586i	−0.815229	+	0.815229i	−0.985412	−	0.170184i	$-0.945564\pi$
$443$	−17.1586	+	17.1586i	−0.815229	+	0.815229i	0.170184	+	0.985412i	$0.445564\pi$
$444$	2.08381	−	7.77688i	0.0988931	−	0.369074i
$445$	15.0163	+	5.87465i	0.711843	+	0.278485i
$446$	23.1523	+	13.3670i	1.09629	+	0.632944i
$447$	34.2054			1.61786
$448$	−14.4276	−	8.32978i	−0.681640	−	0.393545i
$449$	2.37239	+	8.85389i	0.111960	+	0.417841i	0.999042	−	0.0437720i	$-0.0139375\pi$
$449$	2.37239	+	8.85389i	0.111960	+	0.417841i	−0.887081	+	0.461613i	$0.847271\pi$
$450$	−2.35012	+	10.4008i	−0.110786	+	0.490297i
$451$	−1.36735	+	2.36832i	−0.0643860	+	0.111520i
$452$	−33.7475	−	9.04261i	−1.58735	−	0.425329i
$453$	14.1248	+	24.4648i	0.663639	+	1.14946i
$454$	62.2722			2.92258
$455$		0			0
$456$	−5.80989			−0.272073
$457$	10.7399	+	18.6021i	0.502391	+	0.870167i	0.999996	+	0.00276341i	$0.000879623\pi$
$457$	10.7399	+	18.6021i	0.502391	+	0.870167i	−0.497605	+	0.867404i	$0.665787\pi$
$458$	−39.6631	−	10.6277i	−1.85333	−	0.496599i
$459$	6.56877	−	11.3775i	0.306604	−	0.531054i
$460$	0.709072	+	0.887168i	0.0330607	+	0.0413644i
$461$	1.31453	+	4.90591i	0.0612240	+	0.228491i	0.989758	−	0.142757i	$-0.0455967\pi$
$461$	1.31453	+	4.90591i	0.0612240	+	0.228491i	−0.928534	+	0.371248i	$0.878930\pi$
$462$	−27.0180	−	15.5989i	−1.25699	−	0.725725i
$463$	−20.0793			−0.933163			−0.466581	−	0.884478i	$-0.654515\pi$
$463$	−20.0793			−0.933163			−0.466581	+	0.884478i	$0.654515\pi$
$464$	6.14905	+	3.55016i	0.285463	+	0.164812i
$465$	1.34289	−	0.587633i	0.0622748	−	0.0272508i
$466$	−13.4737	+	50.2844i	−0.624156	+	2.32938i
$467$	21.4507	−	21.4507i	0.992618	−	0.992618i	−0.00735447	−	0.999973i	$-0.502341\pi$
$467$	21.4507	−	21.4507i	0.992618	−	0.992618i	0.999973	+	0.00735447i	$0.00234102\pi$
$468$		0			0
$469$		−	7.75807i		−	0.358234i
$470$	14.7559	−	6.45704i	0.680639	−	0.297841i
$471$	−4.31627	−	7.47600i	−0.198883	−	0.344476i
$472$	−0.00142822	−	0.00533020i	−6.57392e−5	−	0.000245342i
$473$		−	36.3934i		−	1.67337i
$474$	−48.2818	+	12.9371i	−2.21766	+	0.594219i
$475$	−6.08820	+	0.241062i	−0.279346	+	0.0110607i
$476$	8.92064	+	8.92064i	0.408877	+	0.408877i
$477$	5.82226	−	1.56007i	0.266583	−	0.0714306i
$478$	−2.15680	+	8.04928i	−0.0986497	+	0.368166i
$479$	30.0497	+	8.05179i	1.37300	+	0.367896i	0.868575	−	0.495557i	$-0.165036\pi$
$479$	30.0497	+	8.05179i	1.37300	+	0.367896i	0.504430	+	0.863453i	$0.331703\pi$
$480$	−22.3664	+	17.8764i	−1.02088	+	0.815943i
$481$		0			0
$482$	−33.1210	−	33.1210i	−1.50862	−	1.50862i
$483$	0.364031	−	0.210173i	0.0165640	−	0.00956321i
$484$	50.0165	−	28.8770i	2.27348	−	1.31259i
$485$	5.54305	−	7.52768i	0.251697	−	0.341814i
$486$	−15.1377	+	15.1377i	−0.686662	+	0.686662i
$487$	−9.71579	+	16.8282i	−0.440264	+	0.762560i	−0.997709	−	0.0676540i	$-0.978449\pi$
$487$	−9.71579	+	16.8282i	−0.440264	+	0.762560i	0.557445	+	0.830214i	$0.311782\pi$
$488$	1.67014	−	2.89277i	0.0756039	−	0.130950i
$489$	12.9321	−	12.9321i	0.584810	−	0.584810i
$490$	−16.0219	+	21.7584i	−0.723797	+	0.982945i
$491$	30.5824	−	17.6568i	1.38017	−	0.796839i	0.387987	−	0.921665i	$-0.373170\pi$
$491$	30.5824	−	17.6568i	1.38017	−	0.796839i	0.992179	+	0.124825i	$0.0398371\pi$
$492$	−2.64131	+	1.52496i	−0.119079	+	0.0687506i
$493$	−22.1234	−	22.1234i	−0.996389	−	0.996389i
$494$		0			0
$495$	−9.03988	+	7.22515i	−0.406312	+	0.324746i
$496$	0.233002	+	0.0624327i	0.0104621	+	0.00280331i
$497$	4.01863	−	14.9977i	0.180260	−	0.672740i
$498$	−11.4702	+	3.07343i	−0.513991	+	0.137723i
$499$	9.44430	+	9.44430i	0.422785	+	0.422785i	0.886161	−	0.463377i	$-0.153362\pi$
$499$	9.44430	+	9.44430i	0.422785	+	0.422785i	−0.463377	+	0.886161i	$0.653362\pi$
$500$	25.9105	−	22.4453i	1.15875	−	1.00378i
$501$	24.2553	−	6.49919i	1.08365	−	0.290363i
$502$			5.32928i			0.237857i
$503$	−6.24460	−	23.3052i	−0.278433	−	1.03913i	−0.953506	−	0.301375i	$-0.902554\pi$
$503$	−6.24460	−	23.3052i	−0.278433	−	1.03913i	0.675073	−	0.737751i	$-0.264112\pi$
$504$	−1.45192	−	2.51480i	−0.0646736	−	0.112018i
$505$	−17.6773	+	7.73542i	−0.786630	+	0.344221i
$506$			2.03659i			0.0905374i
$507$		0			0
$508$	−1.13721	+	1.13721i	−0.0504555	+	0.0504555i
$509$	0.963376	−	3.59537i	0.0427009	−	0.159362i	−0.941283	−	0.337618i	$-0.890379\pi$
$509$	0.963376	−	3.59537i	0.0427009	−	0.159362i	0.983984	+	0.178256i	$0.0570455\pi$
$510$	29.5125	−	12.9144i	1.30683	−	0.571858i
$511$	8.12538	+	4.69119i	0.359446	+	0.207526i
$512$	−8.22064			−0.363304
$513$	−4.30365	−	2.48471i	−0.190011	−	0.109703i
$514$	−0.506841	−	1.89156i	−0.0223558	−	0.0834330i
$515$	2.12445	+	2.65804i	0.0936144	+	0.117127i
$516$	20.2942	−	35.1506i	0.893403	−	1.54742i
$517$	16.8850	+	4.52433i	0.742603	+	0.198980i
$518$	1.89964	+	3.29028i	0.0834656	+	0.144567i
$519$	−27.2503			−1.19615
$520$		0			0
$521$	45.2323			1.98166			0.990832	−	0.135103i	$-0.0431364\pi$
$521$	45.2323			1.98166			0.990832	+	0.135103i	$0.0431364\pi$
$522$	10.3557	+	17.9366i	0.453256	+	0.785062i
$523$	−1.10259	−	0.295439i	−0.0482131	−	0.0129187i	0.234632	−	0.972084i	$-0.424612\pi$
$523$	−1.10259	−	0.295439i	−0.0482131	−	0.0129187i	−0.282845	+	0.959166i	$0.591278\pi$
$524$	−7.81683	+	13.5392i	−0.341480	+	0.591461i
$525$	−6.77362	−	10.7283i	−0.295625	−	0.468221i
$526$	8.84790	+	33.0208i	0.385787	+	1.43978i
$527$	−0.920525	−	0.531466i	−0.0400987	−	0.0231510i
$528$	−7.93430			−0.345296
$529$	19.8948	+	11.4863i	0.864992	+	0.499403i
$530$	−29.8179	−	11.6653i	−1.29521	−	0.506706i
$531$	−0.000563919		0.00210457i	−2.44720e−5		9.13307e-5i
$532$	3.37434	−	3.37434i	0.146296	−	0.146296i
$533$		0			0
$534$			32.2479i			1.39550i
$535$	−11.8337	+	30.2484i	−0.511614	+	1.30775i
$536$	7.28818	+	12.6235i	0.314801	+	0.545252i
$537$	−6.50114	−	24.2626i	−0.280545	−	1.04701i
$538$			54.8782i			2.36597i
$539$	−28.3265	+	7.59005i	−1.22011	+	0.326927i
$540$	27.6423	−	4.19714i	1.18953	−	0.180616i
$541$	22.3573	+	22.3573i	0.961218	+	0.961218i	0.999276	−	0.0380580i	$-0.0121172\pi$
$541$	22.3573	+	22.3573i	0.961218	+	0.961218i	−0.0380580	+	0.999276i	$0.512117\pi$
$542$	28.5171	−	7.64112i	1.22491	−	0.328214i
$543$	4.19929	−	15.6720i	0.180209	−	0.672548i
$544$	20.0551	+	5.37376i	0.859857	+	0.230398i
$545$	−9.32685	−	11.6694i	−0.399518	−	0.499864i
$546$		0			0
$547$	−5.20384	−	5.20384i	−0.222500	−	0.222500i	0.587050	−	0.809550i	$-0.300289\pi$
$547$	−5.20384	−	5.20384i	−0.222500	−	0.222500i	−0.809550	+	0.587050i	$0.800289\pi$
$548$	10.0995	−	5.83096i	0.431430	−	0.249086i
$549$	−1.14218	+	0.659440i	−0.0487472	+	0.0281442i
$550$	61.4242	−	2.43209i	2.61914	−	0.103705i
$551$	−8.36844	+	8.36844i	−0.356507	+	0.356507i
$552$	−0.394887	+	0.683964i	−0.0168075	+	0.0291114i
$553$	7.13781	−	12.3630i	0.303530	−	0.525730i
$554$	19.4608	−	19.4608i	0.826812	−	0.826812i
$555$	5.80505	−	0.881427i	0.246411	−	0.0374145i
$556$	3.92517	−	2.26620i	0.166464	−	0.0961081i
$557$	5.70401	−	3.29321i	0.241687	−	0.139538i	−0.374265	−	0.927322i	$-0.622105\pi$
$557$	5.70401	−	3.29321i	0.241687	−	0.139538i	0.615952	+	0.787784i	$0.288772\pi$
$558$	0.497544	+	0.497544i	0.0210627	+	0.0210627i
$559$		0			0
$560$	0.231518	−	2.07505i	0.00978343	−	0.0876871i
$561$	33.7709	+	9.04887i	1.42581	+	0.382044i
$562$	5.30173	−	19.7863i	0.223640	−	0.834636i
$563$	−28.3543	+	7.59751i	−1.19499	+	0.320197i	−0.800856	−	0.598856i	$-0.795622\pi$
$563$	−28.3543	+	7.59751i	−1.19499	+	0.320197i	−0.394134	+	0.919053i	$0.628955\pi$
$564$	13.7855	+	13.7855i	0.580475	+	0.580475i
$565$	−3.82492	−	25.1908i	−0.160916	−	1.05979i
$566$	−59.4689	+	15.9347i	−2.49967	+	0.669783i
$567$		−	13.9784i		−	0.587039i
$568$	7.55046	+	28.1787i	0.316810	+	1.18235i
$569$	16.9543	+	29.3658i	0.710763	+	1.23108i	0.964571	+	0.263823i	$0.0849835\pi$
$569$	16.9543	+	29.3658i	0.710763	+	1.23108i	−0.253808	+	0.967255i	$0.581683\pi$
$570$	−4.88501	−	11.1634i	−0.204611	−	0.467585i
$571$		−	33.5525i		−	1.40413i	−0.712113	−	0.702065i	$-0.752262\pi$
$571$		−	33.5525i		−	1.40413i	0.712113	−	0.702065i	$-0.247738\pi$
$572$		0			0
$573$	−20.7277	+	20.7277i	−0.865910	+	0.865910i
$574$	0.372500	−	1.39019i	0.0155478	−	0.0580253i
$575$	−0.385424	+	0.733112i	−0.0160733	+	0.0305729i
$576$	−10.7031	−	6.17945i	−0.445964	−	0.257477i
$577$	11.0413			0.459654			0.229827	−	0.973232i	$-0.426184\pi$
$577$	11.0413			0.459654			0.229827	+	0.973232i	$0.426184\pi$
$578$	12.9070	+	7.45188i	0.536862	+	0.309957i
$579$	−7.76326	−	28.9729i	−0.322630	−	1.20407i
$580$	7.38321	−	66.1743i	0.306571	−	2.74774i
$581$	1.69571	−	2.93706i	0.0703499	−	0.121850i
$582$	18.0589	+	4.83886i	0.748565	+	0.200577i
$583$	−17.3748	−	30.0940i	−0.719589	−	1.24636i
$584$	−17.6282			−0.729461
$585$		0			0
$586$	58.8002			2.42902
$587$	−11.7529	−	20.3567i	−0.485095	−	0.840209i	0.514758	−	0.857335i	$-0.327882\pi$
$587$	−11.7529	−	20.3567i	−0.485095	−	0.840209i	−0.999853	+	0.0171260i	$0.994548\pi$
$588$	−31.5916	−	8.46495i	−1.30282	−	0.349089i
$589$	−0.201033	+	0.348199i	−0.00828342	+	0.0143473i
$590$	0.00904086	−	0.00722594i	0.000372206	−	0.000297487i
$591$	−7.90448	−	29.4999i	−0.325147	−	1.21346i
$592$	0.836794	+	0.483123i	0.0343920	+	0.0198563i
$593$	−30.6582			−1.25898			−0.629491	−	0.777007i	$-0.716737\pi$
$593$	−30.6582			−1.25898			−0.629491	+	0.777007i	$0.716737\pi$
$594$	43.4198	+	25.0684i	1.78153	+	1.02857i
$595$	−3.35196	+	8.56804i	−0.137417	+	0.351255i
$596$	13.6622	−	50.9882i	0.559627	−	2.08856i
$597$	16.0948	−	16.0948i	0.658717	−	0.658717i
$598$		0			0
$599$			7.49378i			0.306188i	0.988212	+	0.153094i	$0.0489237\pi$
$599$			7.49378i			0.306188i	−0.988212	+	0.153094i	$0.951076\pi$
$600$	21.1002	+	11.0931i	0.861410	+	0.452875i
$601$	7.04653	+	12.2049i	0.287434	+	0.497850i	0.973196	−	0.229975i	$-0.0738645\pi$
$601$	7.04653	+	12.2049i	0.287434	+	0.497850i	−0.685763	+	0.727825i	$0.740531\pi$
$602$	4.95724	+	18.5007i	0.202042	+	0.754030i
$603$		−	5.75533i		−	0.234375i
$604$	42.1101	−	11.2834i	1.71343	−	0.459113i
$605$	33.9159	+	24.9742i	1.37888	+	1.01534i
$606$	−27.2872	−	27.2872i	−1.10847	−	1.10847i
$607$	−14.5660	+	3.90296i	−0.591218	+	0.158416i	−0.542010	−	0.840372i	$-0.682336\pi$
$607$	−14.5660	+	3.90296i	−0.591218	+	0.158416i	−0.0492080	+	0.998789i	$0.515670\pi$
$608$	2.03268	−	7.58608i	0.0824363	−	0.307656i
$609$	−23.8044	−	6.37837i	−0.964604	−	0.258465i
$610$	6.96260	+	0.776832i	0.281908	+	0.0314530i
$611$		0			0
$612$	6.61779	+	6.61779i	0.267508	+	0.267508i
$613$	−10.3197	+	5.95807i	−0.416808	+	0.240644i	−0.693711	−	0.720254i	$-0.744025\pi$
$613$	−10.3197	+	5.95807i	−0.416808	+	0.240644i	0.276903	+	0.960898i	$0.410692\pi$
$614$	−28.6614	+	16.5477i	−1.15668	+	0.667810i
$615$	−1.79106	−	1.31886i	−0.0722225	−	0.0531814i
$616$	−11.8375	+	11.8375i	−0.476945	+	0.476945i
$617$	19.4158	−	33.6292i	0.781652	−	1.35386i	−0.149326	−	0.988788i	$-0.547710\pi$
$617$	19.4158	−	33.6292i	0.781652	−	1.35386i	0.930979	−	0.365074i	$-0.118956\pi$
$618$	−3.40258	+	5.89344i	−0.136872	+	0.237069i
$619$	14.9567	−	14.9567i	0.601159	−	0.601159i	−0.339461	−	0.940620i	$-0.610245\pi$
$619$	14.9567	−	14.9567i	0.601159	−	0.601159i	0.940620	+	0.339461i	$0.110245\pi$
$620$	−0.339582	−	2.23648i	−0.0136379	−	0.0898191i
$621$	−0.585021	+	0.337762i	−0.0234761	+	0.0135539i
$622$	62.0887	−	35.8469i	2.48953	−	1.43733i
$623$	−6.51241	−	6.51241i	−0.260914	−	0.260914i
$624$		0			0
$625$	22.5712	+	10.7490i	0.902847	+	0.429961i
$626$	−36.8545	−	9.87514i	−1.47300	−	0.394690i
$627$	3.42284	−	12.7742i	0.136695	−	0.510153i
$628$	−12.8681	+	3.44799i	−0.513492	+	0.137590i
$629$	−3.01067	−	3.01067i	−0.120043	−	0.120043i
$630$	3.61128	−	4.90426i	0.143877	−	0.195390i
$631$	37.7256	−	10.1085i	1.50183	−	0.402415i	0.588119	−	0.808775i	$-0.299869\pi$
$631$	37.7256	−	10.1085i	1.50183	−	0.402415i	0.913713	+	0.406360i	$0.133202\pi$
$632$			26.8219i			1.06692i
$633$	1.63726	+	6.11032i	0.0650751	+	0.242864i
$634$	17.5143	+	30.3357i	0.695582	+	1.20478i
$635$	−1.09226	−	0.427310i	−0.0433450	−	0.0169573i
$636$		−	38.7550i		−	1.53674i
$637$		0			0
$638$	84.4296	−	84.4296i	3.34260	−	3.34260i
$639$	2.98122	−	11.1261i	0.117935	−	0.440141i
$640$	14.7637	+	33.7386i	0.583585	+	1.33363i
$641$	7.55607	+	4.36250i	0.298447	+	0.172308i	0.641745	−	0.766918i	$-0.278211\pi$
$641$	7.55607	+	4.36250i	0.298447	+	0.172308i	−0.343298	+	0.939226i	$0.611544\pi$
$642$	−64.9590			−2.56373
$643$	12.8146	+	7.39852i	0.505359	+	0.291769i	0.730924	−	0.682459i	$-0.239089\pi$
$643$	12.8146	+	7.39852i	0.505359	+	0.291769i	−0.225565	+	0.974228i	$0.572423\pi$
$644$	−0.167894	−	0.626588i	−0.00661594	−	0.0246910i
$645$	29.4178	+	3.28220i	1.15832	+	0.129237i
$646$	−4.41809	+	7.65235i	−0.173827	+	0.301078i
$647$	−32.7213	−	8.76765i	−1.28641	−	0.344692i	−0.450113	−	0.892972i	$-0.648616\pi$
$647$	−32.7213	−	8.76765i	−1.28641	−	0.344692i	−0.836295	+	0.548280i	$0.815283\pi$
$648$	13.1318	+	22.7449i	0.515865	+	0.893505i
$649$	0.0125609			0.000493060
$650$		0			0
$651$	−0.837243			−0.0328141
$652$	−14.1119	−	24.4425i	−0.552664	−	0.957242i
$653$	19.5581	+	5.24059i	0.765369	+	0.205080i	0.620325	−	0.784345i	$-0.287001\pi$
$653$	19.5581	+	5.24059i	0.765369	+	0.205080i	0.145044	+	0.989425i	$0.453667\pi$
$654$	14.9382	−	25.8737i	0.584128	−	1.01174i
$655$	−11.3310	−	1.26422i	−0.442739	−	0.0493973i
$656$	−0.0947353	−	0.353557i	−0.00369879	−	0.0138041i
$657$	6.02782	+	3.48016i	0.235168	+	0.135774i
$658$	−9.19981			−0.358646
$659$	−26.2317	−	15.1449i	−1.02184	−	0.589961i	−0.107205	−	0.994237i	$-0.534190\pi$
$659$	−26.2317	−	15.1449i	−1.02184	−	0.589961i	−0.914637	+	0.404276i	$0.867523\pi$
$660$	29.8284	+	68.1652i	1.16107	+	2.65333i
$661$	5.66280	−	21.1339i	0.220257	−	0.822012i	−0.763992	−	0.645226i	$-0.776763\pi$
$661$	5.66280	−	21.1339i	0.220257	−	0.822012i	0.984249	−	0.176786i	$-0.0565700\pi$
$662$	−27.1574	+	27.1574i	−1.05550	+	1.05550i
$663$		0			0
$664$			6.37202i			0.247282i
$665$	3.24096	+	1.26792i	0.125679	+	0.0491677i
$666$	1.40925	+	2.44090i	0.0546074	+	0.0945829i
$667$	0.416380	+	1.55395i	0.0161223	+	0.0601693i
$668$		−	38.7520i		−	1.49936i
$669$	−22.7944	+	6.10774i	−0.881282	+	0.236139i
$670$	−18.1275	+	24.6179i	−0.700326	+	0.951071i
$671$	5.37640	+	5.37640i	0.207553	+	0.207553i
$672$	15.7969	−	4.23277i	0.609379	−	0.163283i
$673$	−0.148622	+	0.554664i	−0.00572895	+	0.0213807i	−0.968731	−	0.248113i	$-0.920190\pi$
$673$	−0.148622	+	0.554664i	−0.00572895	+	0.0213807i	0.963002	+	0.269494i	$0.0868563\pi$
$674$	−77.0386	−	20.6424i	−2.96742	−	0.795117i
$675$	10.8857	+	17.2411i	0.418989	+	0.663610i
$676$		0			0
$677$	−11.5229	−	11.5229i	−0.442862	−	0.442862i	0.450111	−	0.892973i	$-0.351385\pi$
$677$	−11.5229	−	11.5229i	−0.442862	−	0.442862i	−0.892973	+	0.450111i	$0.851385\pi$
$678$	44.1302	−	25.4786i	1.69481	−	0.978498i
$679$	−4.62416	+	2.66976i	−0.177459	+	0.102456i
$680$	−2.59496	−	17.0904i	−0.0995124	−	0.655386i
$681$	−38.8688	+	38.8688i	−1.48946	+	1.48946i
$682$	2.02823	−	3.51300i	0.0776650	−	0.134520i
$683$	−10.0529	+	17.4121i	−0.384663	+	0.666256i	−0.991722	−	0.128400i	$-0.959016\pi$
$683$	−10.0529	+	17.4121i	−0.384663	+	0.666256i	0.607059	+	0.794657i	$0.292349\pi$
$684$	2.50325	−	2.50325i	0.0957143	−	0.0957143i
$685$	6.84843	+	5.04288i	0.261665	+	0.192679i
$686$	30.7929	−	17.7783i	1.17568	−	0.678777i
$687$	31.3902	−	18.1232i	1.19761	−	0.691442i
$688$	3.44440	+	3.44440i	0.131317	+	0.131317i
$689$		0			0
$690$	−1.64623	−	0.183673i	−0.0626709	−	0.00699232i
$691$	41.8571	+	11.2156i	1.59232	+	0.426661i	0.942712	−	0.333608i	$-0.108266\pi$
$691$	41.8571	+	11.2156i	1.59232	+	0.426661i	0.649608	+	0.760269i	$0.274933\pi$
$692$	−10.8842	+	40.6205i	−0.413756	+	1.54416i
$693$	6.38467	−	1.71077i	0.242534	−	0.0649867i
$694$	−20.5310	−	20.5310i	−0.779346	−	0.779346i
$695$	2.66164	+	1.95991i	0.100962	+	0.0743436i
$696$	44.7253	−	11.9841i	1.69531	−	0.454256i
$697$			1.61289i			0.0610926i
$698$	−15.6421	−	58.3773i	−0.592064	−	2.20961i
$699$	−22.9764	−	39.7962i	−0.869046	−	1.50523i
$700$	−18.6976	+	5.81200i	−0.706702	+	0.219673i
$701$		−	8.03468i		−	0.303466i	−0.988422	−	0.151733i	$-0.951515\pi$
$701$		−	8.03468i		−	0.303466i	0.988422	−	0.151733i	$-0.0484853\pi$
$702$		0			0
$703$	−1.13882	+	1.13882i	−0.0429514	+	0.0429514i
$704$	−18.4407	+	68.8216i	−0.695010	+	2.59381i
$705$	−5.17995	+	13.2406i	−0.195088	+	0.498670i
$706$	−45.4404	−	26.2350i	−1.71017	−	0.987369i
$707$	11.0212			0.414495
$708$	0.0121320	+	0.00700440i	0.000455948	+	0.000263242i
$709$	5.88217	+	21.9526i	0.220910	+	0.824446i	0.984002	+	0.178157i	$0.0570134\pi$
$709$	5.88217	+	21.9526i	0.220910	+	0.824446i	−0.763092	+	0.646289i	$0.776320\pi$
$710$	−47.7956	+	38.2008i	−1.79374	+	1.43365i
$711$	5.29519	−	9.17153i	0.198585	−	0.343959i
$712$	16.7146	+	4.47866i	0.626406	+	0.167845i
$713$	0.0273276	+	0.0473328i	0.00102343	+	0.00177263i
$714$	−18.4000			−0.688604
$715$		0			0
$716$	−38.7636			−1.44866
$717$	−3.67794	−	6.37039i	−0.137355	−	0.237906i
$718$	−28.2014	−	7.55655i	−1.05247	−	0.282008i
$719$	−21.4786	+	37.2021i	−0.801018	+	1.38740i	0.117928	+	0.993022i	$0.462375\pi$
$719$	−21.4786	+	37.2021i	−0.801018	+	1.38740i	−0.918946	+	0.394382i	$0.870959\pi$
$720$	0.171752	−	1.53938i	0.00640081	−	0.0573693i
$721$	−0.503026	−	1.87732i	−0.0187336	−	0.0699149i
$722$	−34.1413	−	19.7115i	−1.27061	−	0.733585i
$723$	41.3467			1.53770
$724$	−21.6841	−	12.5193i	−0.805882	−	0.465276i
$725$	46.3705	−	14.4139i	1.72216	−	0.535319i
$726$	−21.8015	+	81.3643i	−0.809129	+	3.01971i
$727$	1.42786	−	1.42786i	0.0529563	−	0.0529563i	−0.680133	−	0.733089i	$-0.738078\pi$
$727$	1.42786	−	1.42786i	0.0529563	−	0.0529563i	0.733089	+	0.680133i	$0.238078\pi$
$728$		0			0
$729$			13.9369i			0.516183i
$730$	−14.8220	−	33.8718i	−0.548586	−	1.25365i
$731$	−10.7322	−	18.5887i	−0.396945	−	0.687528i
$732$	2.19473	+	8.19086i	0.0811197	+	0.302743i
$733$		−	32.1064i		−	1.18588i	−0.805247	−	0.592939i	$-0.797967\pi$
$733$		−	32.1064i		−	1.18588i	0.805247	−	0.592939i	$-0.202033\pi$
$734$	32.3220	−	8.66065i	1.19303	−	0.319670i
$735$	−3.58058	−	23.5816i	−0.132072	−	0.869820i
$736$	−0.754907	−	0.754907i	−0.0278262	−	0.0278262i
$737$	−32.0491	+	8.58752i	−1.18054	+	0.316325i
$738$	0.276339	−	1.03131i	0.0101722	−	0.0379631i
$739$	19.8460	+	5.31771i	0.730046	+	0.195615i	0.604650	−	0.796492i	$-0.293313\pi$
$739$	19.8460	+	5.31771i	0.730046	+	0.195615i	0.125396	+	0.992107i	$0.459980\pi$
$740$	1.00474	−	9.00534i	0.0369351	−	0.331043i
$741$		0			0
$742$	12.9317	+	12.9317i	0.474736	+	0.474736i
$743$	−19.4891	+	11.2520i	−0.714985	+	0.412797i	−0.812904	−	0.582398i	$-0.802115\pi$
$743$	−19.4891	+	11.2520i	−0.714985	+	0.412797i	0.0979193	+	0.995194i	$0.468781\pi$
$744$	1.36232	−	0.786533i	0.0499449	−	0.0288357i
$745$	38.0601	−	5.77897i	1.39442	−	0.211725i
$746$	−9.83771	+	9.83771i	−0.360184	+	0.360184i
$747$	1.25796	−	2.17886i	0.0460265	−	0.0797202i
$748$	26.9773	−	46.7261i	0.986389	−	1.70848i
$749$	13.1184	−	13.1184i	0.479334	−	0.479334i
$750$	−3.57372	+	49.8702i	−0.130494	+	1.82100i
$751$	−1.44204	+	0.832560i	−0.0526207	+	0.0303806i	−0.526080	−	0.850435i	$-0.676339\pi$
$751$	−1.44204	+	0.832560i	−0.0526207	+	0.0303806i	0.473459	+	0.880816i	$0.343005\pi$
$752$	−2.02626	+	1.16986i	−0.0738901	+	0.0426605i
$753$	−3.32640	−	3.32640i	−0.121221	−	0.121221i
$754$		0			0
$755$	19.8498	+	24.8355i	0.722410	+	0.903855i
$756$	−15.4254	−	4.13321i	−0.561015	−	0.150324i
$757$	−10.1014	+	37.6990i	−0.367143	+	1.37019i	0.497350	+	0.867550i	$0.334306\pi$
$757$	−10.1014	+	37.6990i	−0.367143	+	1.37019i	−0.864493	+	0.502645i	$0.832360\pi$
$758$	39.7186	−	10.6426i	1.44265	−	0.386556i
$759$	−1.27119	−	1.27119i	−0.0461412	−	0.0461412i
$760$	−6.46463	+	0.981575i	−0.234497	+	0.0356055i
$761$	15.7109	−	4.20973i	0.569521	−	0.152603i	0.0374441	−	0.999299i	$-0.488078\pi$
$761$	15.7109	−	4.20973i	0.569521	−	0.152603i	0.532077	+	0.846696i	$0.321412\pi$
$762$		−	2.34565i		−	0.0849739i
$763$	2.20841	+	8.24188i	0.0799496	+	0.298376i
$764$	22.6186	+	39.1766i	0.818313	+	1.41736i
$765$	−2.48665	+	6.35620i	−0.0899052	+	0.229809i
$766$			23.0560i			0.833045i
$767$		0			0
$768$	−15.4289	+	15.4289i	−0.556741	+	0.556741i
$769$	10.3296	−	38.5504i	0.372493	−	1.39016i	−0.484479	−	0.874803i	$-0.660991\pi$
$769$	10.3296	−	38.5504i	0.372493	−	1.39016i	0.856973	−	0.515362i	$-0.172342\pi$
$770$	−32.6982	−	12.7921i	−1.17836	−	0.460995i
$771$	1.49702	+	0.864306i	0.0539139	+	0.0311272i
$772$	−46.2891			−1.66598
$773$	17.8304	+	10.2944i	0.641313	+	0.370262i	0.785120	−	0.619343i	$-0.212601\pi$
$773$	17.8304	+	10.2944i	0.641313	+	0.370262i	−0.143807	+	0.989606i	$0.545934\pi$
$774$	3.67753	+	13.7247i	0.132186	+	0.493325i
$775$	1.39494	−	0.880735i	0.0501077	−	0.0316369i
$776$	5.01612	−	8.68818i	0.180068	−	0.311887i
$777$	−3.23942	−	0.868001i	−0.116214	−	0.0311394i
$778$	3.83988	+	6.65087i	0.137666	+	0.238445i
$779$	0.610095			0.0218589
$780$		0			0
$781$	−66.4048			−2.37615
$782$	0.600577	+	1.04023i	0.0214766	+	0.0371986i
$783$	38.2553	+	10.2505i	1.36713	+	0.366322i
$784$	1.96257	−	3.39927i	0.0700917	−	0.121402i
$785$	−6.06575	−	7.58927i	−0.216496	−	0.270873i
$786$	−5.90153	−	22.0248i	−0.210501	−	0.785599i
$787$	−24.8106	−	14.3244i	−0.884404	−	0.510611i	−0.0122960	−	0.999924i	$-0.503914\pi$
$787$	−24.8106	−	14.3244i	−0.884404	−	0.510611i	−0.872108	+	0.489314i	$0.837247\pi$
$788$	−47.1311			−1.67898
$789$	−26.1334	−	15.0881i	−0.930375	−	0.537152i
$790$	−51.5371	+	22.5521i	−1.83361	+	0.802369i
$791$	−3.76666	+	14.0574i	−0.133927	+	0.499822i
$792$	−8.78163	+	8.78163i	−0.312042	+	0.312042i
$793$		0			0
$794$			26.8568i			0.953111i
$795$	25.8927	−	11.3304i	0.918321	−	0.401848i
$796$	−17.5631	−	30.4202i	−0.622508	−	1.07822i
$797$	2.27363	+	8.48530i	0.0805361	+	0.300565i	0.994432	−	0.105385i	$-0.0336075\pi$
$797$	2.27363	+	8.48530i	0.0805361	+	0.300565i	−0.913895	+	0.405950i	$0.866941\pi$
$798$			6.96002i			0.246382i
$799$	9.95859	−	2.66840i	0.352310	−	0.0944011i
$800$	−21.8667	+	23.6698i	−0.773106	+	0.836852i
$801$	−4.83124	−	4.83124i	−0.170703	−	0.170703i
$802$	−8.86190	+	2.37454i	−0.312924	+	0.0838479i
$803$	10.3855	−	38.7592i	0.366496	−	1.36778i
$804$	−35.7433	−	9.57739i	−1.26057	−	0.337768i
$805$	0.369546	−	0.295361i	0.0130248	−	0.0104101i
$806$		0			0
$807$	−34.2536	−	34.2536i	−1.20578	−	1.20578i
$808$	−17.9331	+	10.3537i	−0.630884	+	0.364241i
$809$	−0.820571	+	0.473757i	−0.0288497	+	0.0166564i	−0.514356	−	0.857577i	$-0.671969\pi$
$809$	−0.820571	+	0.473757i	−0.0288497	+	0.0166564i	0.485506	+	0.874233i	$0.338635\pi$
$810$	−32.6620	+	44.3563i	−1.14762	+	1.55852i
$811$	28.8041	−	28.8041i	1.01145	−	1.01145i	0.0115151	−	0.999934i	$-0.496335\pi$
$811$	28.8041	−	28.8041i	1.01145	−	1.01145i	0.999934	−	0.0115151i	$-0.00366545\pi$
$812$	−19.0158	+	32.9363i	−0.667324	+	1.15584i
$813$	−13.0302	+	22.5690i	−0.456991	+	0.791531i
$814$	11.4896	−	11.4896i	0.402711	−	0.402711i
$815$	12.2046	−	16.5743i	0.427509	−	0.580574i
$816$	−4.05261	+	2.33978i	−0.141870	+	0.0819086i
$817$	−7.03139	+	4.05958i	−0.245997	+	0.142027i
$818$	−11.0440	−	11.0440i	−0.386145	−	0.386145i
$819$		0			0
$820$	−2.68133	+	2.14306i	−0.0936361	+	0.0748390i
$821$	−1.29968	−	0.348249i	−0.0453592	−	0.0121540i	0.236068	−	0.971737i	$-0.424141\pi$
$821$	−1.29968	−	0.348249i	−0.0453592	−	0.0121540i	−0.281427	+	0.959583i	$0.590808\pi$
$822$	−4.40224	+	16.4294i	−0.153546	+	0.573041i
$823$	31.9429	−	8.55907i	1.11346	−	0.298350i	0.345225	−	0.938520i	$-0.387803\pi$
$823$	31.9429	−	8.55907i	1.11346	−	0.298350i	0.768234	+	0.640169i	$0.221136\pi$
$824$	2.58211	+	2.58211i	0.0899520	+	0.0899520i
$825$	−36.8214	+	39.8575i	−1.28196	+	1.38766i
$826$	−0.00638537	+	0.00171095i	−0.000222175	+	5.95317e-5i
$827$		−	26.4195i		−	0.918697i	−0.888256	−	0.459349i	$-0.848083\pi$
$827$		−	26.4195i		−	0.918697i	0.888256	−	0.459349i	$-0.151917\pi$
$828$	−0.124552	−	0.464834i	−0.00432848	−	0.0161541i
$829$	−1.23034	−	2.13101i	−0.0427314	−	0.0740130i	0.843869	−	0.536550i	$-0.180273\pi$
$829$	−1.23034	−	2.13101i	−0.0427314	−	0.0740130i	−0.886600	+	0.462537i	$0.846939\pi$
$830$	−12.2435	+	5.35766i	−0.424980	+	0.185967i
$831$			24.2940i			0.842748i
$832$		0			0
$833$	−12.2301	+	12.2301i	−0.423747	+	0.423747i
$834$	−1.71093	+	6.38526i	−0.0592445	+	0.221104i
$835$	25.8907	−	11.3295i	0.895985	−	0.392074i
$836$	−17.6747	−	10.2045i	−0.611292	−	0.352929i
$837$	1.34551			0.0465075
$838$	−41.3802	−	23.8909i	−1.42946	−	0.825297i
$839$	13.0306	+	48.6308i	0.449866	+	1.67892i	0.702759	+	0.711428i	$0.251951\pi$
$839$	13.0306	+	48.6308i	0.449866	+	1.67892i	−0.252893	+	0.967494i	$0.581382\pi$
$840$	−8.50096	−	10.6361i	−0.293311	−	0.366981i
$841$	32.6597	−	56.5682i	1.12619	−	1.95063i
$842$	−9.70754	−	2.60113i	−0.334544	−	0.0896408i
$843$	9.04093	+	15.6594i	0.311386	+	0.539337i
$844$	9.76228			0.336032
$845$		0			0
$846$	−6.82488			−0.234644
$847$	−12.0286	−	20.8342i	−0.413308	−	0.715870i
$848$	4.49261	+	1.20379i	0.154277	+	0.0413384i
$849$	27.1730	−	47.0651i	0.932576	−	1.61527i
$850$	30.6565	−	19.3559i	1.05151	−	0.663900i
$851$	0.0566632	+	0.211470i	0.00194239	+	0.00724909i
$852$	−64.1371	−	37.0296i	−2.19730	−	1.26861i
$853$	42.9612			1.47096			0.735481	−	0.677545i	$-0.236956\pi$
$853$	42.9612			1.47096			0.735481	+	0.677545i	$0.236956\pi$
$854$	−3.46543	−	2.00077i	−0.118585	−	0.0684649i
$855$	2.40431	+	0.940605i	0.0822255	+	0.0321680i
$856$	−9.02166	+	33.6693i	−0.308354	+	1.15079i
$857$	−29.0789	+	29.0789i	−0.993316	+	0.993316i	−0.999978	−	0.00666151i	$-0.997880\pi$
$857$	−29.0789	+	29.0789i	−0.993316	+	0.993316i	0.00666151	+	0.999978i	$0.497880\pi$
$858$		0			0
$859$		−	42.1283i		−	1.43740i	−0.695321	−	0.718700i	$-0.744738\pi$
$859$		−	42.1283i		−	1.43740i	0.695321	−	0.718700i	$-0.255262\pi$
$860$	16.6426	−	42.5406i	0.567508	−	1.45062i
$861$	0.635216	+	1.10023i	0.0216481	+	0.0374956i
$862$	−20.8810	−	77.9289i	−0.711209	−	2.65427i
$863$		−	6.80768i		−	0.231736i	−0.993265	−	0.115868i	$-0.963035\pi$
$863$		−	6.80768i		−	0.231736i	0.993265	−	0.115868i	$-0.0369650\pi$
$864$	−25.3867	+	6.80234i	−0.863672	+	0.231420i
$865$	−30.3212	+	4.60391i	−1.03095	+	0.156537i
$866$	−12.8806	−	12.8806i	−0.437702	−	0.437702i
$867$	−12.7075	+	3.40497i	−0.431570	+	0.115639i
$868$	−0.334410	+	1.24803i	−0.0113506	+	0.0423610i
$869$	−58.9734	−	15.8019i	−2.00054	−	0.536042i
$870$	60.6323	+	75.8612i	2.05563	+	2.57194i
$871$		0			0
$872$	−11.3361	−	11.3361i	−0.383888	−	0.383888i
$873$	−3.43044	+	1.98056i	−0.116103	+	0.0670320i
$874$	0.393479	−	0.227175i	0.0133096	−	0.00768432i
$875$	−9.34949	−	10.7929i	−0.316071	−	0.364867i
$876$	31.6443	−	31.6443i	1.06916	−	1.06916i
$877$	−23.8407	+	41.2933i	−0.805043	+	1.39437i	0.111219	+	0.993796i	$0.464524\pi$
$877$	−23.8407	+	41.2933i	−0.805043	+	1.39437i	−0.916262	+	0.400579i	$0.868809\pi$
$878$	32.2621	−	55.8796i	1.08879	−	1.88585i
$879$	−36.7017	+	36.7017i	−1.23792	+	1.23792i
$880$	−8.82845	+	1.34049i	−0.297607	+	0.0451880i
$881$	−4.43737	+	2.56192i	−0.149499	+	0.0863133i	−0.572884	−	0.819637i	$-0.694175\pi$
$881$	−4.43737	+	2.56192i	−0.149499	+	0.0863133i	0.423385	+	0.905950i	$0.360842\pi$
$882$	9.91554	−	5.72474i	0.333873	−	0.192762i
$883$	14.8283	+	14.8283i	0.499014	+	0.499014i	0.911131	−	0.412117i	$-0.135211\pi$
$883$	14.8283	+	14.8283i	0.499014	+	0.499014i	−0.412117	+	0.911131i	$0.635211\pi$
$884$		0			0
$885$	−0.00113283	+	0.0101533i	−3.80796e−5	+	0.000341301i
$886$	−52.7568	−	14.1361i	−1.77240	−	0.474913i
$887$	−2.72597	+	10.1735i	−0.0915293	+	0.341592i	−0.996470	−	0.0839449i	$-0.973248\pi$
$887$	−2.72597	+	10.1735i	−0.0915293	+	0.341592i	0.904941	+	0.425537i	$0.139915\pi$
$888$	6.08644	−	1.63086i	0.204248	−	0.0547280i
$889$	0.473700	+	0.473700i	0.0158874	+	0.0158874i
$890$	5.44825	+	35.8820i	0.182626	+	1.20277i
$891$	−57.7457	+	15.4729i	−1.93455	+	0.518362i
$892$			36.4179i			1.21936i
$893$	−1.00935	−	3.76695i	−0.0337767	−	0.126056i
$894$	38.4949	+	66.6751i	1.28746	+	2.22995i
$895$	−11.3329	−	25.8985i	−0.378818	−	0.865691i
$896$		−	21.0349i		−	0.702725i
$897$		0			0
$898$	−14.5886	+	14.5886i	−0.486828	+	0.486828i
$899$	0.829344	−	3.09515i	0.0276602	−	0.103229i
$900$	−13.8708	+	4.31163i	−0.462361	+	0.143721i
$901$	−17.7490	−	10.2474i	−0.591307	−	0.341391i
$902$	−6.15528			−0.204948
$903$	−14.6418	−	8.45347i	−0.487250	−	0.281314i
$904$	−7.07704	−	26.4119i	−0.235379	−	0.878446i
$905$	2.02476	−	18.1476i	0.0673053	−	0.603245i
$906$	−31.7921	+	55.0656i	−1.05622	+	1.82943i
$907$	−20.8031	−	5.57417i	−0.690755	−	0.185087i	−0.103669	−	0.994612i	$-0.533058\pi$
$907$	−20.8031	−	5.57417i	−0.690755	−	0.185087i	−0.587086	+	0.809525i	$0.699725\pi$
$908$	42.4147	+	73.4645i	1.40758	+	2.43800i
$909$	8.17608			0.271184
$910$		0			0
$911$	−16.6400			−0.551309			−0.275654	−	0.961257i	$-0.588895\pi$
$911$	−16.6400			−0.551309			−0.275654	+	0.961257i	$0.588895\pi$
$912$	0.885047	+	1.53295i	0.0293068	+	0.0507609i
$913$	−14.0102	−	3.75401i	−0.463669	−	0.124240i
$914$	−24.1734	+	41.8696i	−0.799586	+	1.38492i
$915$	−4.83077	+	3.86101i	−0.159700	+	0.127641i
$916$	−14.4774	−	54.0305i	−0.478347	−	1.78522i
$917$	5.63968	+	3.25607i	0.186239	+	0.107525i
$918$	29.5701			0.975958
$919$	5.95358	+	3.43730i	0.196390	+	0.113386i	0.594971	−	0.803747i	$-0.297164\pi$
$919$	5.95358	+	3.43730i	0.196390	+	0.113386i	−0.398580	+	0.917133i	$0.630497\pi$
$920$	−0.323833	+	0.827758i	−0.0106765	+	0.0272904i
$921$	7.56111	−	28.2184i	0.249147	−	0.929829i
$922$	−8.08349	+	8.08349i	−0.266216	+	0.266216i
$923$		0			0
$924$		−	42.4987i		−	1.39810i
$925$	6.31033	−	1.96152i	0.207482	−	0.0644942i
$926$	−22.5973	−	39.1396i	−0.742593	−	1.28621i
$927$	−0.373170	−	1.39269i	−0.0122565	−	0.0457419i
$928$			62.5915i			2.05467i
$929$	42.9399	−	11.5057i	1.40881	−	0.377490i	0.527312	−	0.849672i	$-0.323200\pi$
$929$	42.9399	−	11.5057i	1.40881	−	0.377490i	0.881501	+	0.472182i	$0.156533\pi$
$930$	2.65674	+	1.95630i	0.0871178	+	0.0641497i
$931$	4.62617	+	4.62617i	0.151617	+	0.151617i
$932$	−68.4993	+	18.3543i	−2.24377	+	0.601216i
$933$	−16.3795	+	61.1290i	−0.536240	+	2.00127i
$934$	65.9535	+	17.6722i	2.15806	+	0.578252i
$935$	39.1054	+	4.36307i	1.27888	+	0.142688i
$936$		0			0
$937$	13.1724	+	13.1724i	0.430323	+	0.430323i	0.888738	−	0.458415i	$-0.151583\pi$
$937$	13.1724	+	13.1724i	0.430323	+	0.430323i	−0.458415	+	0.888738i	$0.651583\pi$
$938$	15.1225	−	8.73096i	0.493766	−	0.285076i
$939$	29.1675	−	16.8399i	0.951846	−	0.549548i
$940$	17.6681	+	13.0100i	0.576270	+	0.424339i
$941$	40.0251	−	40.0251i	1.30478	−	1.30478i	0.379650	−	0.925130i	$-0.376045\pi$
$941$	40.0251	−	40.0251i	1.30478	−	1.30478i	0.925130	−	0.379650i	$-0.123955\pi$
$942$	9.71510	−	16.8270i	0.316535	−	0.548255i
$943$	0.0414669	−	0.0718228i	0.00135035	−	0.00233887i
$944$	−0.00118881	+	0.00118881i	−3.86925e−5	+	3.86925e-5i
$945$	−1.74830	−	11.5143i	−0.0568723	−	0.374559i
$946$	70.9401	−	40.9573i	2.30646	−	1.33164i
$947$	−51.0040	+	29.4472i	−1.65741	+	0.956904i	−0.683501	+	0.729949i	$0.739544\pi$
$947$	−51.0040	+	29.4472i	−1.65741	+	0.956904i	−0.973905	+	0.226955i	$0.927123\pi$
$948$	−48.1479	−	48.1479i	−1.56377	−	1.56377i
$949$		0			0
$950$	−7.32157	−	11.5962i	−0.237543	−	0.376229i
$951$	−29.8668	−	8.00278i	−0.968497	−	0.259508i
$952$	−2.55544	+	9.53703i	−0.0828223	+	0.309097i
$953$	17.2456	−	4.62094i	0.558640	−	0.149687i	0.0315583	−	0.999502i	$-0.489953\pi$
$953$	17.2456	−	4.62094i	0.558640	−	0.149687i	0.527081	+	0.849815i	$0.323286\pi$
$954$	9.59336	+	9.59336i	0.310596	+	0.310596i
$955$	−19.5616	+	26.5654i	−0.632999	+	0.859638i
$956$	−10.9650	+	2.93807i	−0.354634	+	0.0950240i
$957$			105.398i			3.40703i
$958$	18.1230	+	67.6360i	0.585528	+	2.18522i
$959$	−2.42886	−	4.20691i	−0.0784320	−	0.135848i
$960$	−53.9673	−	21.1129i	−1.74179	−	0.681417i
$961$			30.8911i			0.996488i
$962$		0			0
$963$	9.73187	−	9.73187i	0.313605	−	0.313605i
$964$	16.5146	−	61.6333i	0.531899	−	1.98507i
$965$	−13.5331	−	30.9263i	−0.435645	−	0.995554i
$966$	0.819363	+	0.473059i	0.0263626	+	0.0152204i
$967$	−23.2093			−0.746360			−0.373180	−	0.927759i	$-0.621733\pi$
$967$	−23.2093			−0.746360			−0.373180	+	0.927759i	$0.621733\pi$
$968$	39.1446	+	22.6001i	1.25815	+	0.726395i
$969$	−2.01875	−	7.53407i	−0.0648515	−	0.242029i
$970$	20.9115	+	2.33314i	0.671429	+	0.0749127i
$971$	−21.1932	+	36.7078i	−0.680123	+	1.17801i	0.294820	+	0.955553i	$0.404740\pi$
$971$	−21.1932	+	36.7078i	−0.680123	+	1.17801i	−0.974943	+	0.222455i	$0.928593\pi$
$972$	−28.1691	−	7.54788i	−0.903523	−	0.242098i
$973$	−0.943975	−	1.63501i	−0.0302624	−	0.0524161i
$974$	−43.7367			−1.40141
$975$		0			0
$976$	−1.01768			−0.0325752
$977$	12.2049	+	21.1395i	0.390469	+	0.676312i	0.992511	−	0.122152i	$-0.0389796\pi$
$977$	12.2049	+	21.1395i	0.390469	+	0.676312i	−0.602043	+	0.798464i	$0.705646\pi$
$978$	39.7618	+	10.6541i	1.27144	+	0.340682i
$979$	−19.6945	+	34.1118i	−0.629438	+	1.09022i
$980$	−36.5819	−	4.08152i	−1.16857	−	0.130379i
$981$	1.63831	+	6.11424i	0.0523071	+	0.195213i
$982$	68.8352	+	39.7420i	2.19662	+	1.26822i
$983$	−4.47004			−0.142572			−0.0712860	−	0.997456i	$-0.522710\pi$
$983$	−4.47004			−0.142572			−0.0712860	+	0.997456i	$0.522710\pi$
$984$	−2.06718	−	1.19349i	−0.0658992	−	0.0380469i
$985$	−13.7792	−	31.4889i	−0.439043	−	1.00332i
$986$	18.2264	−	68.0220i	0.580448	−	2.16626i
$987$	5.74230	−	5.74230i	0.182779	−	0.182779i
$988$		0			0
$989$			1.10369i			0.0350952i
$990$	−24.2572	−	9.48982i	−0.770944	−	0.301606i
$991$	24.7675	+	42.8986i	0.786766	+	1.36272i	0.927938	+	0.372734i	$0.121580\pi$
$991$	24.7675	+	42.8986i	0.786766	+	1.36272i	−0.141172	+	0.989985i	$0.545087\pi$
$992$	0.550363	+	2.05398i	0.0174740	+	0.0652140i
$993$		−	33.9020i		−	1.07585i
$994$	33.7570	−	9.04516i	1.07071	−	0.286895i
$995$	15.1894	−	20.6278i	0.481536	−	0.653945i
$996$	−11.4384	−	11.4384i	−0.362439	−	0.362439i
$997$	33.8485	−	9.06967i	1.07199	−	0.287239i	0.320681	−	0.947187i	$-0.396088\pi$
$997$	33.8485	−	9.06967i	1.07199	−	0.287239i	0.751311	+	0.659948i	$0.229422\pi$
$998$	−7.78071	+	29.0380i	−0.246294	+	0.919182i
$999$	5.20597	+	1.39494i	0.164710	+	0.0441338i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.o.e.587.5		20
5.3	odd	4		845.2.t.f.418.5		20
13.2	odd	12		845.2.f.d.437.10		20
13.3	even	3		845.2.k.e.577.1		20
13.4	even	6		845.2.o.g.357.1		20
13.5	odd	4		845.2.t.g.427.5		20
13.6	odd	12		845.2.t.e.657.1		20
13.7	odd	12		845.2.t.f.657.5		20
13.8	odd	4		65.2.t.a.37.1	yes	20
13.9	even	3		65.2.o.a.32.5	✓	20
13.10	even	6		845.2.k.d.577.10		20
13.11	odd	12		845.2.f.e.437.1		20
13.12	even	2		845.2.o.f.587.1		20
39.8	even	4		585.2.dp.a.37.5		20
39.35	odd	6		585.2.cf.a.487.1		20
65.3	odd	12		845.2.f.e.408.10		20
65.8	even	4		65.2.o.a.63.5	yes	20
65.9	even	6		325.2.s.b.32.1		20
65.18	even	4		845.2.o.g.258.1		20
65.22	odd	12		325.2.x.b.318.5		20
65.23	odd	12		845.2.f.d.408.1		20
65.28	even	12		845.2.k.d.268.10		20
65.33	even	12	inner	845.2.o.e.488.5		20
65.34	odd	4		325.2.x.b.232.5		20
65.38	odd	4		845.2.t.e.418.1		20
65.43	odd	12		845.2.t.g.188.5		20
65.47	even	4		325.2.s.b.193.1		20
65.48	odd	12		65.2.t.a.58.1	yes	20
65.58	even	12		845.2.o.f.488.1		20
65.63	even	12		845.2.k.e.268.1		20
195.8	odd	4		585.2.cf.a.388.1		20
195.113	even	12		585.2.dp.a.253.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.5	✓	20	13.9	even	3
65.2.o.a.63.5	yes	20	65.8	even	4
65.2.t.a.37.1	yes	20	13.8	odd	4
65.2.t.a.58.1	yes	20	65.48	odd	12
325.2.s.b.32.1		20	65.9	even	6
325.2.s.b.193.1		20	65.47	even	4
325.2.x.b.232.5		20	65.34	odd	4
325.2.x.b.318.5		20	65.22	odd	12
585.2.cf.a.388.1		20	195.8	odd	4
585.2.cf.a.487.1		20	39.35	odd	6
585.2.dp.a.37.5		20	39.8	even	4
585.2.dp.a.253.5		20	195.113	even	12
845.2.f.d.408.1		20	65.23	odd	12
845.2.f.d.437.10		20	13.2	odd	12
845.2.f.e.408.10		20	65.3	odd	12
845.2.f.e.437.1		20	13.11	odd	12
845.2.k.d.268.10		20	65.28	even	12
845.2.k.d.577.10		20	13.10	even	6
845.2.k.e.268.1		20	65.63	even	12
845.2.k.e.577.1		20	13.3	even	3
845.2.o.e.488.5		20	65.33	even	12	inner
845.2.o.e.587.5		20	1.1	even	1	trivial
845.2.o.f.488.1		20	65.58	even	12
845.2.o.f.587.1		20	13.12	even	2
845.2.o.g.258.1		20	65.18	even	4
845.2.o.g.357.1		20	13.4	even	6
845.2.t.e.418.1		20	65.38	odd	4
845.2.t.e.657.1		20	13.6	odd	12
845.2.t.f.418.5		20	5.3	odd	4
845.2.t.f.657.5		20	13.7	odd	12
845.2.t.g.188.5		20	65.43	odd	12
845.2.t.g.427.5		20	13.5	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.o (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.12540 + 1.94926i) q^{2} +(-1.91913 - 0.514229i) q^{3} +(-1.53307 + 2.65535i) q^{4} +(-2.22228 - 0.247944i) q^{5} +(-1.15743 - 4.31958i) q^{6} +(1.10607 + 0.638592i) q^{7} -2.39966 q^{8} +(0.820542 + 0.473740i) q^{9} +(-2.01765 - 4.61083i) q^{10} +(1.41373 - 5.27612i) q^{11} +(4.30760 - 4.30760i) q^{12} +2.87469i q^{14} +(4.13734 + 1.61860i) q^{15} +(0.365551 + 0.633152i) q^{16} +(-0.833802 - 3.11179i) q^{17} +2.13259i q^{18} +(-1.17707 + 0.315395i) q^{19} +(4.06528 - 5.52081i) q^{20} +(-1.79431 - 1.79431i) q^{21} +(11.8755 - 3.18204i) q^{22} +(-0.0428736 + 0.160006i) q^{23} +(4.60524 + 1.23397i) q^{24} +(4.87705 + 1.10200i) q^{25} +(2.88358 + 2.88358i) q^{27} +(-3.39137 + 1.95801i) q^{28} +(8.41068 - 4.85591i) q^{29} +(1.50111 + 9.88630i) q^{30} +(0.233305 - 0.233305i) q^{31} +(-3.22244 + 5.58143i) q^{32} +(-5.42627 + 9.39857i) q^{33} +(5.12732 - 5.12732i) q^{34} +(-2.29967 - 1.69337i) q^{35} +(-2.51589 + 1.45255i) q^{36} +(1.14457 - 0.660816i) q^{37} +(-1.93947 - 1.93947i) q^{38} +(5.33270 + 0.594981i) q^{40} +(-0.483595 - 0.129579i) q^{41} +(1.47825 - 5.51690i) q^{42} +(6.43569 - 1.72444i) q^{43} +(11.8426 + 11.8426i) q^{44} +(-1.70601 - 1.25623i) q^{45} +(-0.360144 + 0.0965002i) q^{46} +3.20027i q^{47} +(-0.375953 - 1.40308i) q^{48} +(-2.68440 - 4.64952i) q^{49} +(3.34056 + 10.7468i) q^{50} +6.40069i q^{51} +(4.49845 - 4.49845i) q^{53} +(-2.37565 + 8.86603i) q^{54} +(-4.44989 + 11.3745i) q^{55} +(-2.65420 - 1.53240i) q^{56} +2.42113 q^{57} +(18.9308 + 10.9297i) q^{58} +(0.000595178 + 0.00222123i) q^{59} +(-10.6407 + 8.50465i) q^{60} +(-0.695993 + 1.20550i) q^{61} +(0.717332 + 0.192209i) q^{62} +(0.605053 + 1.04798i) q^{63} -13.0440 q^{64} -24.4270 q^{66} +(-3.03718 - 5.26055i) q^{67} +(9.54117 + 2.55655i) q^{68} +(0.164560 - 0.285026i) q^{69} +(0.712764 - 6.38837i) q^{70} +(-3.14648 - 11.7428i) q^{71} +(-1.96902 - 1.13681i) q^{72} +7.34614 q^{73} +(2.57620 + 1.48737i) q^{74} +(-8.79299 - 4.62280i) q^{75} +(0.967044 - 3.60906i) q^{76} +(4.93298 - 4.93298i) q^{77} -11.1774i q^{79} +(-0.655369 - 1.49768i) q^{80} +(-5.47236 - 9.47841i) q^{81} +(-0.291657 - 1.08848i) q^{82} -2.65539i q^{83} +(7.51533 - 2.01373i) q^{84} +(1.08139 + 7.12201i) q^{85} +(10.6041 + 10.6041i) q^{86} +(-18.6382 + 4.99409i) q^{87} +(-3.39247 + 12.6609i) q^{88} +(-6.96542 - 1.86638i) q^{89} +(0.528764 - 4.73922i) q^{90} +(-0.359145 - 0.359145i) q^{92} +(-0.567713 + 0.327769i) q^{93} +(-6.23815 + 3.60160i) q^{94} +(2.69398 - 0.409048i) q^{95} +(9.05440 - 9.05440i) q^{96} +(-2.09035 + 3.62059i) q^{97} +(6.04207 - 10.4652i) q^{98} +(3.65954 - 3.65954i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 4 q^{6} + 6 q^{7} + 12 q^{8} + 12 q^{9} + 2 q^{10} + 8 q^{11} + 24 q^{12} + 12 q^{15} - 2 q^{16} - 4 q^{17} - 16 q^{19} + 8 q^{20} + 4 q^{21} + 16 q^{22} + 10 q^{23}+ \cdots - 60 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 4 * q^6 + 6 * q^7 + 12 * q^8 + 12 * q^9 + 2 * q^10 + 8 * q^11 + 24 * q^12 + 12 * q^15 - 2 * q^16 - 4 * q^17 - 16 * q^19 + 8 * q^20 + 4 * q^21 + 16 * q^22 + 10 * q^23 + 28 * q^24 - 18 * q^25 + 4 * q^27 - 6 * q^28 + 26 * q^30 - 6 * q^32 - 18 * q^33 - 2 * q^34 + 40 * q^35 - 36 * q^36 - 42 * q^37 + 8 * q^38 - 16 * q^40 + 28 * q^41 + 40 * q^42 - 10 * q^43 + 36 * q^44 - 32 * q^45 - 8 * q^46 - 56 * q^48 - 18 * q^49 + 8 * q^50 - 10 * q^53 - 12 * q^54 - 10 * q^55 - 12 * q^57 + 90 * q^58 - 8 * q^59 - 92 * q^60 - 16 * q^61 + 44 * q^62 - 32 * q^63 - 20 * q^64 - 32 * q^66 - 58 * q^67 + 22 * q^68 + 16 * q^69 + 32 * q^70 + 56 * q^71 + 66 * q^72 + 72 * q^73 + 18 * q^74 + 38 * q^75 + 80 * q^76 + 28 * q^77 + 68 * q^80 - 14 * q^81 - 56 * q^82 - 32 * q^84 + 6 * q^85 + 60 * q^86 - 34 * q^87 - 82 * q^88 + 6 * q^89 - 46 * q^90 - 8 * q^92 - 48 * q^93 - 48 * q^94 + 26 * q^95 + 56 * q^96 - 22 * q^97 + 4 * q^98 - 60 * q^99

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